Geometric Sequences and Series

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

•  $\frac{1}{3}$  

•  $\frac{1}{12}$  

•  $\frac{1}{16}$  

•  $\frac{1}{4}$  

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

Evaluate the geometric series described below.
 $a_1=-1,\ r\ =\ 4,\ n\ =\ 8$  

• -585

• 585

• -21,845

• 21,845

Tags

CCSS.HSA.SSE.B.4

What is the sum of the first ten terms of the sequence 4, -12, 36, -144 . . . ?

• 59,050
• -59,048
• -78,732
• 118,096

Tags

CCSS.HSA.SSE.B.4

Evaluate  $\sum_{k\ =\ 1}^7\left(-2\right)^{k\ -1\ }$  

• 44

•  $\frac{1}{3}$  

• 43

• 49

Tags

CCSS.HSA.SSE.B.4

Find the sum of the infinite geometric series:

200 - 100 + 50 - 25 + ...

• 525 / 2

• 400 / 3

• 3 / 400

• 2 / 525

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

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

• yes
• no

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.BF.A.2

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

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.2

Find a₁₂ in the sequence -1, -3, -9, -27, ...

• -177,147
• -19,683
• -59,049
• 118,098

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.2

CCSS.HSF.IF.A.3