sequences and series
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SEQUENCE AND
SERIES ZONE
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Competence
Motivation
Sequences
SEQUENCES AND
SERIES
Standard Competence:
Using sequences and series concept to
solve problems
Series
Test
Refferences
Exit
For Senior High School
Competence
references
Motivation
Sequences
Series
Test
Refferences
Exit
Olive, Jenny. 2003. Maths a Student’s Survival
Guide.
United Kingdom : Cambridge
University Press
Urban, Paul. 2004. Mathematics for International
Student.
Australia : Haese & Harris
Publications
For Senior High School
Basic Competence
Competence
Motivation
Sequences
Series
1. Determine nth terms sequences and number of n terms
in arithmetic and geometry
2. Design mathematics model of problems related to
sequences and series
3. Solve the mathematics model of problems related to
sequences and series
Test
Refferences
Exit
Indicators
1.
2.
3.
4.
Explaining definition of sequences and series
Finding formula of arithmetic sequences and series
Finding formula of geometry sequences and series
Calculating nth terms and the number of n terms in
arithmetic and geometry series
5. Identifying problems related to series
6. Formulating mathematics model from series problems
7. Solving problems related to series
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Competence
NUMBER SEQUENCES
Motivation
Sequences
Series
Test
Refferences
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MOTIVATION
Competence
Look at the picture below!!
Motivation
Sequences
Series
Test
Refferences
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Motivation
Sequences
Series
Test
Refferences
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Consider to the illustrated of
amoeba. Every 5 minutes, amoeba
split self become 2 such that after
15 minutes they form this number
1, 2, 4, .....
Can you help me to determine how many
amoeba after 60minutes??????
That’s why we will learn this material.
For Senior High School
Number Sequences
Let see here!!!
1st row
2nd row
3rd row
.
.
If you represents un as the number of bricks in row n (from the
top) then
u1 = 3, u2 = 4, u3 = 5, u4 = 6,………
So,
The number pattern: 3,4,5,6…… is called a sequence of
You can specified this sequences by using an explicit
numbers
formula
Un = n + 2 for n = 1,2,3,4,5,…. etc
Check:
u1 = 1+2 = 3 √
√
u2 = 2 + 2= 4 √
u3 = 3+2 = 5
etc
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Definition:
NUMBER
SEQUENCES
A number sequences is a set of numbers defined by a rule for
positive integers.
Example:
3,5, 7,9,11,…..
Un = {2n+1}
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Definition:
ARITHMETIC
SEQUENCES
An arithmetic sequence is a sequence in which each term
differs from the previous one by the same fixed number
Example
2, 5, 8,11,14,…..
Is arithmetic sequence as 5 – 2 = 8 – 5 = 11 – 8 = 14 – 11
etc
For all positive
integer n where d
is a contant
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ARITHMETIC
SEQUENCES
GENERAL FORMULA
Suppose the first term of an arithmetics
sequences is U1 and the common diference is d.
Then,
.
.
.
It is the general term
for arithmetic
sequence with first
term U11 and common
diference d
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Example:
1. Consider the sequence 2, 9, 16, 23,
30, .....
a. Show that the sequence is
arithmetic.
b. Find the formula for the general
term Un
c. Find the 100th term of the
sequence.
How to
solve
it???
Let see
here!
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Solution:
a. 9 – 2 = 7
16 – 9 = 7
23 – 16 = 7
30 – 23 = 7
From the pattern we can find that the
common difference d is 7.
So, the sequence is arithmetics with U1
=2 d=7
b.
So, the general formula is
c. If n = 100 so
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Definition
GEOMETRIC
SEQUENCES
Geometric sequence is a sequence that each term can be
obtained from the previous one by multiplying by the same non
zero constan.
Example
2, 4, 8, 16,32,…..
Is a geometric sequence as 2 x 2 = 4 , 4 x 2 = 8, 8
x 2= 16 etc
For all positive
integer n where r is a
ratio
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GEOMETRIC
SEQUENCES
GENERAL FORMULA
Suppose the first term of an arithmetics
sequences is U1 and the common diference
is d.
Then,
.
.
.
It is the general term
for arithmetic
sequence with first
term U1 and common
diference d
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Example
:
Solve the
problem beside!
For the sequence
a. Show that the sequence is geometric
b. Find the general term un
c. Hence, find the 12th term as a fraction
Solution:
a.
The common ratio of the sequence is
So, the sequence is geometric with u1 = 8 and r =
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b.
Or
So,the general formula is
Or
c. If n = 12 so,
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Competence
ARITHMETICS SERIES
Motivation
Sequences
Series
Test
Refferences
Author
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ARITHMETIC SERIES
Definition:
An arithmetic series is the addition of successive terms of
an arithmetic sequence.
Example:
2, 5, 8, 11,….. , 14
Is an arithmetic
sequence.
So,
2 + 5 +8 +11 +….. + 14
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Is an
arithmetic
series.
Next
ARITHMETIC SERIES
SUM OF AN ARITHMETIC SERIES
Recall
If the first term is u1 and the
common difference is d, then
the term are??????
u1, , u1 + d , u1 + 2d , u1 + 3d ,
etc.
Now,
Suppose that un is the last term of an arithmetic
series.
Then,
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ARITHMETIC SERIES
Sn = u1 + (u1 + d ) + (u1 + 2d ) + .... + (un - 2d ) + (un
–S d =
)+
u+
n (u - d ) + (u - 2d ) + .... + (u + 2d )+ (u +
u
n
n
n
n
1
1
+
d ) + u1
2Sn = (u1 + un)+ (u1 + un) + (u1 + un) + .... + (u1 + un) + (u1 + un)
+ (u1 + un)
n times
2Sn = n(u1 + un)
Where
So,
or
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Example:
Find the sum of 4 + 7 + 10 + 13 + . . . To 50 term.
Solution:
The series is arithmetic with u1 = 4, d = 3 and n = 50.
So,
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GEOMETRIC SERIES
Definition:
A geometric series is the addition of successive terms of a
geometric sequence.
Recall that if the first term is u1 and the common ratio is r, then the
terms are:
So ,
…………………(*)
Multiply Sn by r, the whole sequence get shifted along by one. We
get :
…………………..(**)
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GEOMETRIC SERIES
Subtracting (*) and (**) makes nearly everything disappear, then
we get:
Factoring, then we get:
So, the sum of a
geometric series is:
For
Or
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EXAMPLE
:
Find the sum of 2 + 6 + 18 + 54 + ……….. to 12 terms!!
SOLUTION:
The series is geometric with u1 = 2 , r = 3 and n = 12
So:
Using
Then,
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GEOMETRIC SERIES
Sum to Infinity of Geometric Series
when n gets
Sometime it is necessary to consider
very large. What happens to Sn in this situation???
i.e.,
then rn approaches 0 for every large
n
This mean that the series converges and has a sum to infinity
of
So, the sum to infinity of geometric series is
If
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EXAMPLE :
Find the sum of this infinite geometric series !!
SOLUTION:
The series is geometric with u1 = 1, r = ½ So:
Using
Then,
So, the sum of this infinite geometric series is 2
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Motivation
Sequences
Series
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FINAL TEST
DO YOUR BEST!!!
Click Here
Final Test
Sequence and Series
Problem 1
Consider the sequence 6,17,28,39,50,…………
The general term and the 50th of this sequence is…………
A
and 545
C
B
and 542
D
Home
and 549
and 535
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Final Test
Sequence and Series
Problem 1
Consider the sequence 6,17,28,39,50,…………
The general term and the 50th of this sequence is…………
A
and 545
C
B
and 542
D
and 549
and 535
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 1
Consider the sequence 6,17,28,39,50,…………
The general term and the 50th of this sequence is…………
A
and 545
C
B
and 542
D
and 549
and 535
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 2
A sequence is defined by un = 3n -2, the least term of the
sequence which is greater than 450 is……………
A
C
B
D
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Final Test
Sequence and Series
Problem 2
A sequence is defined by un = 3n -2, the least term of the
sequence which is greater than 450 is……………
A
C
B
E
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 2
A sequence is defined by un = 3n -2, the least term of the
sequence which is greater than 450 is……………
A
C
B
D
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 3
The initial population of rabbits on a farm was 50. the
population increased by 7% each week. How many rabbits
when present after 30 weeks??? (using up rounding)
A 380 rabbits
C 320 rabbits
B 381 rabbits
D 370 rabbits
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Final Test
Sequence and Series
Problem 3
The initial population of rabbits on a farm was 50. the
population increased by 7% each week. How many rabbits
when present after 30 weeks??? (using up rounding)
A 380 rabbits
C 320 rabbits
B 381 rabbits
D 370 rabbits
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 3
The initial population of rabbits on a farm was 50. the
population increased by 7% each week. How many rabbits
when present after 30 weeks??? (using up rounding)
A 380 rabbits
C 320 rabbits
B 381 rabbits
D 370 rabbits
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 4
A nest of ants initially consist of 500 ants. The population is
increasing by 12% each weeks. After 10 weeks the population
will be………
A 1542 ants
C 1543 ants
B 1552 ants
D 1553 ants
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Final Test
Sequence and Series
Problem 4
A nest of ants initially consist of 500 ants. The population is
increasing by 12% each weeks. After 10 weeks the population
will be………
A 1542 ants
C 1543 ants
B 1552 ants
D 1553 ants
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 4
A nest of ants initially consist of 500 ants. The population is
increasing by 12% each weeks. After 10 weeks the population
will be………
A 1542 ants
C 1543 ants
B 1552 ants
D 1553 ants
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 5
The geometric sequence has u2 = - 6 and u5 = 162. the
general term of that sequence is………
A
C
B
D
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Final Test
Sequence and Series
Problem 5
The geometric sequence has u2 = - 6 and u5 = 162. the
general term of that sequence is………
A
C
B
D
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 5
The geometric sequence has u2 = - 6 and u5 = 162. the
general term of that sequence is………
A
C
B
D
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 6
The sum of 2 + 6 + 18 + 54 + ……… to 12 terms is…………
A
B
Home
531.442
531.440
C 530.442
D 531.402
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Final Test
Sequence and Series
Problem 6
The sum of 2 + 6 + 18 + 54 + ……… to 12 terms is…………
A
B
531.442
531.440
C 530.442
D 531.402
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 6
The sum of 2 + 6 + 18 + 54 + ……… to 12 terms is…………
A
B
531.442
531.440
C 530.442
D 531.402
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 7
The general formula of 9 – 3 + 1 – 1/3 + ……… to n terms
is………
A
C
B
D
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Final Test
Sequence and Series
Problem 7
The general formula of 9 – 3 + 1 – 1/3 + ……… to n terms
is………
A
C
B
D
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 7
The general formula of 9 – 3 + 1 – 1/3 + ……… to n terms
is………
A
C
B
D
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 8
A ball takes 1 second to hit the ground when dropped. It then
takes 90% of this time to rebound to its new height and this
continues until the ball comes to rest. How long does it take
for the ball to come to rest???
Home
A
9 seconds
C 10 seconds
B
8 seconds
D 11 seconds
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Final Test
Sequence and Series
Problem 8
A ball takes 1 second to hit the ground when dropped. It then
takes 90% of this time to rebound to its new height and this
continues until the ball comes to rest. How long does it take
for the ball to come to rest???
A
9 seconds
C 10 seconds
B
8 seconds
D 11 seconds
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 8
A ball takes 1 second to hit the ground when dropped. It then
takes 90% of this time to rebound to its new height and this
continues until the ball comes to rest. How long does it take
for the ball to come to rest???
A
9 seconds
C 10 seconds
B
8 seconds
D 11 seconds
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 9
The sum of -6 + 1 + 8 + 15 + …… + 141 is………
A
1356
C
1478
B
1565
D
1485
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Final Test
Sequence and Series
Problem 9
The sum of -6 + 1 + 8 + 15 + …… + 141 is………
A
1356
C
1478
B
1565
D
1485
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 9
The sum of -6 + 1 + 8 + 15 + …… + 141 is………
A
1356
C
1478
B
1565
D
1485
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 10
An arithmetic series has seven terms. The first term is 5 and
the last term is 53. the sum of the series is…………
A
B
Home
230
203
C 215
D 204
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Final Test
Sequence and Series
Problem 10
An arithmetic series has seven terms. The first term is 5 and
the last term is 53. the sum of the series is…………
A
B
230
203
C 215
D 204
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 10
An arithmetic series has seven terms. The first term is 5 and
the last term is 53. the sum of the series is…………
A
B
230
203
C 215
D 204
FALSE!! DON’T GIVE UP!!!
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THAT’S ALL FOR
TODAY
THANKS FOR YOUR
ATTENTION
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SEQUENCE AND
SERIES ZONE
ENTER
Competence
Motivation
Sequences
SEQUENCES AND
SERIES
Standard Competence:
Using sequences and series concept to
solve problems
Series
Test
Refferences
Exit
For Senior High School
Competence
references
Motivation
Sequences
Series
Test
Refferences
Exit
Olive, Jenny. 2003. Maths a Student’s Survival
Guide.
United Kingdom : Cambridge
University Press
Urban, Paul. 2004. Mathematics for International
Student.
Australia : Haese & Harris
Publications
For Senior High School
Basic Competence
Competence
Motivation
Sequences
Series
1. Determine nth terms sequences and number of n terms
in arithmetic and geometry
2. Design mathematics model of problems related to
sequences and series
3. Solve the mathematics model of problems related to
sequences and series
Test
Refferences
Exit
Indicators
1.
2.
3.
4.
Explaining definition of sequences and series
Finding formula of arithmetic sequences and series
Finding formula of geometry sequences and series
Calculating nth terms and the number of n terms in
arithmetic and geometry series
5. Identifying problems related to series
6. Formulating mathematics model from series problems
7. Solving problems related to series
For Senior High School
Competence
NUMBER SEQUENCES
Motivation
Sequences
Series
Test
Refferences
Exit
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MOTIVATION
Competence
Look at the picture below!!
Motivation
Sequences
Series
Test
Refferences
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Competence
Motivation
Sequences
Series
Test
Refferences
Exit
Consider to the illustrated of
amoeba. Every 5 minutes, amoeba
split self become 2 such that after
15 minutes they form this number
1, 2, 4, .....
Can you help me to determine how many
amoeba after 60minutes??????
That’s why we will learn this material.
For Senior High School
Number Sequences
Let see here!!!
1st row
2nd row
3rd row
.
.
If you represents un as the number of bricks in row n (from the
top) then
u1 = 3, u2 = 4, u3 = 5, u4 = 6,………
So,
The number pattern: 3,4,5,6…… is called a sequence of
You can specified this sequences by using an explicit
numbers
formula
Un = n + 2 for n = 1,2,3,4,5,…. etc
Check:
u1 = 1+2 = 3 √
√
u2 = 2 + 2= 4 √
u3 = 3+2 = 5
etc
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Definition:
NUMBER
SEQUENCES
A number sequences is a set of numbers defined by a rule for
positive integers.
Example:
3,5, 7,9,11,…..
Un = {2n+1}
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Definition:
ARITHMETIC
SEQUENCES
An arithmetic sequence is a sequence in which each term
differs from the previous one by the same fixed number
Example
2, 5, 8,11,14,…..
Is arithmetic sequence as 5 – 2 = 8 – 5 = 11 – 8 = 14 – 11
etc
For all positive
integer n where d
is a contant
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ARITHMETIC
SEQUENCES
GENERAL FORMULA
Suppose the first term of an arithmetics
sequences is U1 and the common diference is d.
Then,
.
.
.
It is the general term
for arithmetic
sequence with first
term U11 and common
diference d
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Example:
1. Consider the sequence 2, 9, 16, 23,
30, .....
a. Show that the sequence is
arithmetic.
b. Find the formula for the general
term Un
c. Find the 100th term of the
sequence.
How to
solve
it???
Let see
here!
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Solution:
a. 9 – 2 = 7
16 – 9 = 7
23 – 16 = 7
30 – 23 = 7
From the pattern we can find that the
common difference d is 7.
So, the sequence is arithmetics with U1
=2 d=7
b.
So, the general formula is
c. If n = 100 so
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Definition
GEOMETRIC
SEQUENCES
Geometric sequence is a sequence that each term can be
obtained from the previous one by multiplying by the same non
zero constan.
Example
2, 4, 8, 16,32,…..
Is a geometric sequence as 2 x 2 = 4 , 4 x 2 = 8, 8
x 2= 16 etc
For all positive
integer n where r is a
ratio
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GEOMETRIC
SEQUENCES
GENERAL FORMULA
Suppose the first term of an arithmetics
sequences is U1 and the common diference
is d.
Then,
.
.
.
It is the general term
for arithmetic
sequence with first
term U1 and common
diference d
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Example
:
Solve the
problem beside!
For the sequence
a. Show that the sequence is geometric
b. Find the general term un
c. Hence, find the 12th term as a fraction
Solution:
a.
The common ratio of the sequence is
So, the sequence is geometric with u1 = 8 and r =
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b.
Or
So,the general formula is
Or
c. If n = 12 so,
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Competence
ARITHMETICS SERIES
Motivation
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Series
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Author
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ARITHMETIC SERIES
Definition:
An arithmetic series is the addition of successive terms of
an arithmetic sequence.
Example:
2, 5, 8, 11,….. , 14
Is an arithmetic
sequence.
So,
2 + 5 +8 +11 +….. + 14
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Is an
arithmetic
series.
Next
ARITHMETIC SERIES
SUM OF AN ARITHMETIC SERIES
Recall
If the first term is u1 and the
common difference is d, then
the term are??????
u1, , u1 + d , u1 + 2d , u1 + 3d ,
etc.
Now,
Suppose that un is the last term of an arithmetic
series.
Then,
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ARITHMETIC SERIES
Sn = u1 + (u1 + d ) + (u1 + 2d ) + .... + (un - 2d ) + (un
–S d =
)+
u+
n (u - d ) + (u - 2d ) + .... + (u + 2d )+ (u +
u
n
n
n
n
1
1
+
d ) + u1
2Sn = (u1 + un)+ (u1 + un) + (u1 + un) + .... + (u1 + un) + (u1 + un)
+ (u1 + un)
n times
2Sn = n(u1 + un)
Where
So,
or
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Example:
Find the sum of 4 + 7 + 10 + 13 + . . . To 50 term.
Solution:
The series is arithmetic with u1 = 4, d = 3 and n = 50.
So,
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GEOMETRIC SERIES
Definition:
A geometric series is the addition of successive terms of a
geometric sequence.
Recall that if the first term is u1 and the common ratio is r, then the
terms are:
So ,
…………………(*)
Multiply Sn by r, the whole sequence get shifted along by one. We
get :
…………………..(**)
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GEOMETRIC SERIES
Subtracting (*) and (**) makes nearly everything disappear, then
we get:
Factoring, then we get:
So, the sum of a
geometric series is:
For
Or
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EXAMPLE
:
Find the sum of 2 + 6 + 18 + 54 + ……….. to 12 terms!!
SOLUTION:
The series is geometric with u1 = 2 , r = 3 and n = 12
So:
Using
Then,
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GEOMETRIC SERIES
Sum to Infinity of Geometric Series
when n gets
Sometime it is necessary to consider
very large. What happens to Sn in this situation???
i.e.,
then rn approaches 0 for every large
n
This mean that the series converges and has a sum to infinity
of
So, the sum to infinity of geometric series is
If
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EXAMPLE :
Find the sum of this infinite geometric series !!
SOLUTION:
The series is geometric with u1 = 1, r = ½ So:
Using
Then,
So, the sum of this infinite geometric series is 2
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Series
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FINAL TEST
DO YOUR BEST!!!
Click Here
Final Test
Sequence and Series
Problem 1
Consider the sequence 6,17,28,39,50,…………
The general term and the 50th of this sequence is…………
A
and 545
C
B
and 542
D
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and 549
and 535
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Final Test
Sequence and Series
Problem 1
Consider the sequence 6,17,28,39,50,…………
The general term and the 50th of this sequence is…………
A
and 545
C
B
and 542
D
and 549
and 535
TRUE!! CONGRATULATION!!!
Home
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Final Test
Sequence and Series
Problem 1
Consider the sequence 6,17,28,39,50,…………
The general term and the 50th of this sequence is…………
A
and 545
C
B
and 542
D
and 549
and 535
FALSE!! DON’T GIVE UP!!!
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Back
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Final Test
Sequence and Series
Problem 2
A sequence is defined by un = 3n -2, the least term of the
sequence which is greater than 450 is……………
A
C
B
D
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Final Test
Sequence and Series
Problem 2
A sequence is defined by un = 3n -2, the least term of the
sequence which is greater than 450 is……………
A
C
B
E
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 2
A sequence is defined by un = 3n -2, the least term of the
sequence which is greater than 450 is……………
A
C
B
D
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 3
The initial population of rabbits on a farm was 50. the
population increased by 7% each week. How many rabbits
when present after 30 weeks??? (using up rounding)
A 380 rabbits
C 320 rabbits
B 381 rabbits
D 370 rabbits
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Final Test
Sequence and Series
Problem 3
The initial population of rabbits on a farm was 50. the
population increased by 7% each week. How many rabbits
when present after 30 weeks??? (using up rounding)
A 380 rabbits
C 320 rabbits
B 381 rabbits
D 370 rabbits
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 3
The initial population of rabbits on a farm was 50. the
population increased by 7% each week. How many rabbits
when present after 30 weeks??? (using up rounding)
A 380 rabbits
C 320 rabbits
B 381 rabbits
D 370 rabbits
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 4
A nest of ants initially consist of 500 ants. The population is
increasing by 12% each weeks. After 10 weeks the population
will be………
A 1542 ants
C 1543 ants
B 1552 ants
D 1553 ants
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Final Test
Sequence and Series
Problem 4
A nest of ants initially consist of 500 ants. The population is
increasing by 12% each weeks. After 10 weeks the population
will be………
A 1542 ants
C 1543 ants
B 1552 ants
D 1553 ants
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 4
A nest of ants initially consist of 500 ants. The population is
increasing by 12% each weeks. After 10 weeks the population
will be………
A 1542 ants
C 1543 ants
B 1552 ants
D 1553 ants
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 5
The geometric sequence has u2 = - 6 and u5 = 162. the
general term of that sequence is………
A
C
B
D
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Final Test
Sequence and Series
Problem 5
The geometric sequence has u2 = - 6 and u5 = 162. the
general term of that sequence is………
A
C
B
D
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 5
The geometric sequence has u2 = - 6 and u5 = 162. the
general term of that sequence is………
A
C
B
D
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 6
The sum of 2 + 6 + 18 + 54 + ……… to 12 terms is…………
A
B
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531.442
531.440
C 530.442
D 531.402
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Final Test
Sequence and Series
Problem 6
The sum of 2 + 6 + 18 + 54 + ……… to 12 terms is…………
A
B
531.442
531.440
C 530.442
D 531.402
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 6
The sum of 2 + 6 + 18 + 54 + ……… to 12 terms is…………
A
B
531.442
531.440
C 530.442
D 531.402
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 7
The general formula of 9 – 3 + 1 – 1/3 + ……… to n terms
is………
A
C
B
D
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Final Test
Sequence and Series
Problem 7
The general formula of 9 – 3 + 1 – 1/3 + ……… to n terms
is………
A
C
B
D
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 7
The general formula of 9 – 3 + 1 – 1/3 + ……… to n terms
is………
A
C
B
D
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 8
A ball takes 1 second to hit the ground when dropped. It then
takes 90% of this time to rebound to its new height and this
continues until the ball comes to rest. How long does it take
for the ball to come to rest???
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A
9 seconds
C 10 seconds
B
8 seconds
D 11 seconds
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Final Test
Sequence and Series
Problem 8
A ball takes 1 second to hit the ground when dropped. It then
takes 90% of this time to rebound to its new height and this
continues until the ball comes to rest. How long does it take
for the ball to come to rest???
A
9 seconds
C 10 seconds
B
8 seconds
D 11 seconds
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 8
A ball takes 1 second to hit the ground when dropped. It then
takes 90% of this time to rebound to its new height and this
continues until the ball comes to rest. How long does it take
for the ball to come to rest???
A
9 seconds
C 10 seconds
B
8 seconds
D 11 seconds
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 9
The sum of -6 + 1 + 8 + 15 + …… + 141 is………
A
1356
C
1478
B
1565
D
1485
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Final Test
Sequence and Series
Problem 9
The sum of -6 + 1 + 8 + 15 + …… + 141 is………
A
1356
C
1478
B
1565
D
1485
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 9
The sum of -6 + 1 + 8 + 15 + …… + 141 is………
A
1356
C
1478
B
1565
D
1485
FALSE!! DON’T GIVE UP!!!
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Final Test
Sequence and Series
Problem 10
An arithmetic series has seven terms. The first term is 5 and
the last term is 53. the sum of the series is…………
A
B
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230
203
C 215
D 204
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Final Test
Sequence and Series
Problem 10
An arithmetic series has seven terms. The first term is 5 and
the last term is 53. the sum of the series is…………
A
B
230
203
C 215
D 204
TRUE!! CONGRATULATION!!!
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Final Test
Sequence and Series
Problem 10
An arithmetic series has seven terms. The first term is 5 and
the last term is 53. the sum of the series is…………
A
B
230
203
C 215
D 204
FALSE!! DON’T GIVE UP!!!
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