Geometric Sequences & Series

Given the sequence below, determine if it is geometric. If it is, find the common ratio.

1, 2, 4, 8, ...

• Yes, it is geometric.

  Common ratio: 2

• Yes, it is geometric.

  Common ratio: 1, 3, 5,...

• Yes it is geometric.

  Common ratio: -2

• No, it is not geometric

Given the sequence below, find the explicit formula.

1, 2, 4, 8, ...

• $a_n=-2^{n-1}$

• $a_n=-2\cdot2^{n-1}$

• $a_n=1\cdot\left(-2\right)^{n-1}$

• $a_n=1\cdot2^{n-1}$

Given the sequence below, find the 8^th term.

1, 2, 4, 8,...

• a₈ = -128

• a₈ = -256

• a₈ = 128

• a₈ = 256

Find the next three terms given the sequence below:

2, 8, 32, 128, ...

• 1250, -6250, 31250

• 512, 2048, 8192

• -1250, -6250, -31250

• -1875, -9375, -46875

Find the next three terms given the sequence below:

1, -4, 16, -64, ...

• 32, 64, 128

• 256, -1024, 4096

• 16, 32, 64

• -256, -1024, -4096

Evaluate the geometric series described below.

2 - 6 + 18 - 54...; n = 7

• 1094

• 1237

• 1/2

• 1093

Evaluate the geometric series described below:

4 + 12 + 36 + 108...; n = 7

• 2950

• -2

• 3616

• 4372

 $\sum_{k=1}^{10}\ 2^{k-1}$  

• 904

• 1073

• 1023

• -1

 $\sum_{x=1}^7\ 2\cdot6^{x-1}$  

• 111974

• 118579

• -2/5

• 125858