1. The 10th term of the geometric sequence 2, 6, 18, 54, 162, ... is 39,366. The common ratio is 3. 2. The common ratio of a geometric sequence with a first term of -1 and a fourth term of -8 is 2. 3. The common ratio of a geometric sequence with a first term of -5 and a fifth term of -80 is 2.

1. Activity:
Geometric sequence
Subtitle

2. 1. Find the 10th term of the geometric sequence
2, 6, 18, 54, 162, …
A. Identify the given
information.
A1 = 2
r =
6
2
= 3
n = 10
B. Solution
An = A1rn – 1
A10 = 2(3)10 – 1
A10 = 2(3)9
A10 = 2(19,683)
A10 = 39, 366

3. 2. Find the common ratio of a geometric sequence whose
first term is -1 and the 4th term is -8.
A.Identify the given
A1 = -1
A4 = -8
B. Solution
An = A1rn – 1
-8 = -1(r)4 – 1
-8 = -1(r)3
−8
−1
=
−1
−1
r3
8 = r3
3
8 = 3
r3
3
8 = r
2 = r

4. 3. What is the common ratio of a geometric sequence whose
first term is -5 and the fifth term is -80.
Solution:
A1 = -5
A5 = -80
An = A1rn – 1
-80 = -5r5 – 1
-80 = -5r4
−80
−5
= r4
16 = r3
4
16 =
4
r4
2 = r