Finite geometric series

SUM OF FINITE GEOMETRIC SEQUENCE

1. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
GEOMETRIC
SERIES
(FINITE)(FINITE)

2. 4
2
5
1
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0011 0010 1010 1101 0001 0100 1011
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Identify whether the geometric sequence shown shows a
finite or infinite sequence.Idendetideif
3, 6, 12, 24fydeifdetide
48, 24, 12, …Indetyde edeIwi
36, 18, … , 3/2idefdeyde
2, 4, 8, …ytdehirdegdehI
81, -27, 9, -3omfdeomofdeomoofde
0.4, 0.04, 0.004, …Idehndetidehif
3, -6, 12, -24

3. 4
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0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
WANT SUM?WANT SUM?
Do the following with a partner.
Consider the geometric sequence
3, 6, 12, 24, 48, 96, ...
What is the sum of the first 5 terms?

4. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
Let S
n
= 3 + 6 + 12 + 24 + 48
Multiplying both sides by the common ratio 2, we
get
2S
n
= 6 + 12 + 24 + 48 + 96
Subtracting 2S
n
from S
n
, we have
S
n
= 3 + 6 + 12 + 24 + 48
2S
n
= 6 + 12 + 24 + 48 + 96
-S
n
= 3 - 96
SS
nn = 93 = 93

5. 4
2
5
1
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0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
81, 27, 9, 3, 1, ...
find the sum of the first 4 terms
Let S
n
= 81 + 27 + 9 + 3
Multiplying both sides by the common ratio 1/3,
we get
1/3S
n
= 27 + 9 + 3 + 1
Subtracting 1/3S
n
from S
n
, we have
S
n
= 81 + 27 + 9 + 3
1/3S
n
= 27 + 9 + 3 + 1
2/3S
n
= 81 - 1
2/3S
n = 80 S
n = 3/2(80) SS
nn = 120 = 120

6. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock

7. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock

8. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
SS
nn = = aa
11 – a – a
11rr
nn
1 - r1 - r
SS
nn = = aa
11 – a – a
nnrr
1 - r1 - r
GEOMETRIC SERIES
(FINITE)(FINITE)
r ≠ 1 r ≠ 1

9. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
What if r= 1? S
n
= na
1

What if r= -1? n is even
S
n
= a
1

n is odd
S
n
= 0

10. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock

11. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock

12. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
Execise
A. Fill in the table with the correct values.
Find Me Please
-2188-2188
-39,321-39,321

13. 4
2
5
1
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0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
Individual Activity
1. Find the sum of the first ten terms in the
geometric sequence 3, 6, 12,24,…
2. Find the sum of the first six terms in the
geometric sequence 36, 18, 9, …
Execise
Answer: 3069Answer: 3069

14. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
A student saved PhP 10.00 on Sunday
and doubled his savings each day
thereafter. How much did he save on the
7
th
day? What was his total savings for
the week?
Php 1,270.00Php 1,270.00
ApplicationApplication

15. 4
2
5
1
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0011 0010 1010 1101 0001 0100 1011
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GeneralizationGeneralization
1. What is finite geometric sequence?
2. How do you find the sum of the
terms of a finite geometric sequence?

16. 4
2
5
1
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0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
Evaluation:Evaluation:
1. Find the sum of the first 8 terms of the geometric
sequence: 2, 4, 8, 16, …
2. What is the sum of the first 3 terms of the geometric sequence:
1,
,...
8
1
,
4
1
,
2
1
?
3. What is the sum of the first 30 terms of 1, ,...
8
1
,
4
1
,
2
1
?Do as directed.

17. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock
How do you find the sum of the How do you find the sum of the
terms of an infinite geometric terms of an infinite geometric
sequence? sequence?
ASSIGNMENTASSIGNMENT

18. 4
2
5
1
3
0011 0010 1010 1101 0001 0100 1011
Richpaul_rock