Name:
Date:
School:
Facilitator:
9.08 Geometric Sequences and Series
1. Determine if the sequence is geometric. If it is, find the common ratio.
a)
-3, -15, -75, -375, …
5
b) -1, 1, 4, 8, …
not geometric
c) 1, -5, 25, -125, …
-5
2. Given the following explicit formula for a geometric sequence
a
n
=−
4
(
3
)
n
−
1
What is the 1
st
term?
-4
What is the ratio?
3
What is the 9
th
term?
-26244
3. Given the sequence
2, 12, 72, 432, … find the explicit formula and the value of the 9
th
term.
Explicit Formula
a
n
=
2
×
(
6
)
(
n
−
1
)
9
th
term
3359232
4. Evaluate the geometric series
∑
n
=
1
7
5
(
4
)
n
−
1
What is the value of a?
5
What is the ratio?
4
What is the value of n?
7
What is the sum?
27305
5. Find the number of terms in the geometric series described.
-4 + 16 – 64 + 256 …
S
n
= 52428
What is the value of a?
-4
What is the ratio?
16/(-4)=-4
What is the sum?
52428
What is the value of n?
n/a
6.
Find the sum of the geometric series
1 + 0.5 + 0.25 + 0.125 … if possible.
What is the sum?
2
7. Find the sum of the geometric series
∑
n
=
1
∞
6
(
1
2
)
n
−
1
if possible.
What is the sum?
12
