This document discusses geometric sequences and how to calculate the sum of finite geometric sequences. It provides examples of finding the sum of terms for specific geometric sequences. The key steps shown are using the common ratio r to set up an equation relating the overall sum Sn to itself, then solving this equation to find a closed form for Sn in terms of the first term a1 and common ratio r.

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GEOMETRIC
SERIES
(FINITE)(FINITE)

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Identify whether the geometric sequence shown shows a
finite or infinite sequence.
3, 6, 12, 243, 6, 12, 24
48, 24, 12, …48, 24, 12, …
36, 18, … , 3/236, 18, … , 3/2
2, 4, 8, …2, 4, 8, …
81, -27, 9, -381, -27, 9, -3
0.4, 0.04, 0.004, …0.4, 0.04, 0.004, …
3, -6, 12, -243, -6, 12, -24

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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?

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Let Sn = 3 + 6 + 12 + 24 + 48
Multiplying both sides by the common ratio 2, we
get
2Sn = 6 + 12 + 24 + 48 + 96
Subtracting 2Sn from Sn , we have
Sn = 3 + 6 + 12 + 24 + 48
2Sn = 6 + 12 + 24 + 48 + 96
-Sn = 3 - 96
SSnn = 93= 93

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81, 27, 9, 3, 1, ...
find the sum of the first 4 terms
Let Sn = 81 + 27 + 9 + 3
Multiplying both sides by the common ratio 1/3,
we get
1/3Sn = 27 + 9 + 3 + 1
Subtracting 1/3Sn from Sn , we have
Sn = 81 + 27 + 9 + 3
1/3Sn = 27 + 9 + 3 + 1
2/3Sn = 81 - 1
2/3Sn = 80 Sn = 3/2(80) SSnn = 120= 120

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SSnn == aa11 – a– a11rrnn
1 - r1 - r
SSnn == aa11 – a– annrr
1 - r1 - r
GEOMETRIC SERIES
(FINITE)(FINITE)
r ≠ 1r ≠ 1

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What if r= 1? Sn = na1
What if r= -1? n is even
Sn = a1
n is odd
Sn = 0

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Execise
A. Fill in the table with the correct values.
Find Me Please
-2188-2188
-39,321-39,321

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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

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A student saved PhP 10.00 on Sunday
and doubled his savings each day
thereafter. How much did he save on the
7th
day? What was his total savings for
the week?
Php 1,270.00Php 1,270.00
ApplicationApplication

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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?

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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.

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How do you find the sum of theHow do you find the sum of the
terms of an infinite geometricterms of an infinite geometric
sequence?sequence?
ASSIGNMENTASSIGNMENT

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