# Geometric Sequences and Series

Find the next two terms in the geometric sequence shown below.

5, 15, 45, …

75, 105

135, 405

55, 65

675, 30375

Find the next two terms in the geometric sequence shown below.

16, 8, 4, …

2, 1

1, 0

2, ½

0,-4

Find three geometric means between 9 and 144.

42.75, 76.5, 110.25

2304, 36864, 589824

18, 36, 72

27, 81, 243

Write an equation for the nth term in the sequence.

200, 50, 12.5…

 A. an = 200 • 4n – 1 B. an = 200 • (-4)n – 1 C. an = 200 • (-1/4)n – 1 D. an = 200 • (1/4)n – 1

Find the 15th term in the geometric sequence shown below.

1, 3, 9,…

4782969

14348907

43

1594323

Find the sum for the geometric series shown below.

198.4375

96.875

196.875

396.875

Find the sum for the geometric series shown below.

126

124

252

254

If S6 = 189 and r = 2, what is a1?

9

6

3

3/2

If S8 = 1530 and r = 2, what is a1?

3

6

9

12

A portion of John’s parental family tree is shown below. Find a rule for the number of people in the nth generation.

 A. An = 2(2)n – 1 B. An = 1(2)n – 1 C. An = 2(2)n D. An = 1(2)n

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