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Lesson 1.4 Exercises, pages 48–53
A
3. Write a geometric series for each geometric sequence.

a) 1, 4, 16, 64, 256, . . .
1 ؉ 4 ؉ 16 ؉ 64 ؉ 256 ؉ . . .

b) 20, -10, 5, -2.5, 1.25, . . .
20 ؊ 10 ؉ 5 ؊ 2.5 ؉ 1.25 ؊ . . .

4. Which series appear to be geometric? If the series could be geometric,

determine S5.
a) 2 + 4 + 8 + 16 + 32 + . . .
The series could be geometric.
S5 is: 2 ؉ 4 ؉ 8 ؉ 16 ؉ 32 ‫26 ؍‬

c) 1 + 4 + 9 + 16 + 25 + . . .
The series is not geometric.

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b) 2 - 4 + 8 - 16 + 32 - . . .
The series could be geometric.
S5 is: 2 ؊ 4 ؉ 8 ؊ 16 ؉ 32 ‫22 ؍‬

d) -3 + 9 - 27 + 81 - 243 + . . .
The series could be geometric.
S5 is: ؊3 ؉ 9 ؊ 27 ؉ 81 ؊ 243 ‫381؊ ؍‬

1.4 Geometric Series—Solutions

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5. Use the given data about each geometric series to determine the

indicated value.
a) t1 = 1, r = 0.3; determine S8
Use: Sn ‫؍‬

t1(1 ؊ rn)
,r Z 1
1؊r

Use: Sn ‫؍‬

t1(1 ؊ rn)
,r Z 1
1؊r

Substitute:

Substitute: n ‫ ,8 ؍‬t1 ‫ ,1 ؍‬r ‫3.0 ؍‬
S8 ‫؍‬

1

3

b) t1 = 4 , r = 2 ; determine S4

3
4

n ‫ ,4 ؍‬t1 ‫ , ؍‬r ‫؍‬

1(1 ؊ 0.38)
1 ؊ 0.3

S8 Џ 1.428

S4 ‫؍‬

3
1 4 a1 ؊ a b b
4
2
1؊

S4 ‫؍‬

1
2

1
2

45
, or approximately 1.406
32

B
6. Determine S6 for each geometric series.

a) 2 + 10 + 50 + . . .

b) 80 - 40 + 20 - . . .
؊ 40

10
‫5؍‬
2 n t1(1 ؊ r )
Use: Sn ‫؍‬
,r Z 1
1؊r

80 t1(1 ؊ r )
Use: Sn ‫؍‬
,r Z 1
1؊r

Substitute: n ‫ ,6 ؍‬t1 ‫ ,2 ؍‬r ‫5 ؍‬

Substitute: n ‫ ,6 ؍‬t1 ‫ ,08 ؍‬r ‫5.0؊ ؍‬

t1 ‫ 2 ؍‬and r is:

S6 ‫؍‬

2(1 ؊ 56)
1؊5

t1 ‫ 08 ؍‬and r is:

S6 ‫؍‬

S6 ‫2187 ؍‬

‫5.0 ؊ ؍‬

n

80(1 ؊ (؊0.5)6 )
1 ؊ (؊0.5)

S6 ‫5.25 ؍‬

7. Determine S10 for each geometric series. Give the answers to

3 decimal places.
1
1
1
a) 0.1 +