Sequences and Series

Find the common ratio of the geometric sequence:
 $2,\ \frac{1}{2},\ \frac{1}{8},\ \frac{1}{32},\ ...$  

•  $\frac{1}{3}$  

•  $\frac{1}{12}$  

•  $\frac{1}{16}$  

•  $\frac{1}{4}$  

Is the sequence -432, 72, -12, 2,...geometric?

• yes
• no

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

• 1024, 2048, 4096

• 32, 8, 2

• 64, 32, 16

• 92, 66, 38

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

• 20, 100, 500, 2500
• 5, 20, 80, 320
• 4, 20, 100, 500
• 4, 9, 14, 19

Find an explicit rule for the nth term of the sequence.

• a_n= -2(4)^n-1

• a_n= -2(4)ⁿ

• a_n= 2(-4)^n-1

• a_n= 2(4)^n-1

What is the common ratio for the sequence:
28, 14, 7, 3.5...

• 2
• 1/2
• -14
• -7

Write the recursive formula for 6, 17, 28, 39, 50....

• a_n=a_n-1+11
  a₁=6
• a_n=a_n-1-4
  a₁=6
• a_n=a_n-1+9
  a₁=6
• a_n=a_n-1+6
  a₁=6

Determine if the following sequence is arithmetic or geometric.

4, 9, 14, 19, 24, ...

• Arithmetic

• Geometric

Determine if the following sequence is arithmetic or geometric.

6, 12, 24, 48, 96, ...

• Arithmetic

• Geometric