Geometric series

Multiple Choice

Find the common ratio of the following geometric sequence:

2, -10, 50, -250, ...

• r = -5

• r = 3

• r = 5

• r = -3

Multiple Choice

Find the common ratio of the following geometric sequence:

2, -10, 50, -250, ...

• r = -5

• r = 3

• r = 5

• r = -3

Multiple Choice

Write the explicit formula for the following geometric sequence:

100, 50, 25, 12.5, ...

• a_n = 2(100)^n-1

• a_n = 100(2)^n-1

• a_n = 100(1/2)^n-1

• a_n = (1/2)(100)^n-1

Multiple Choice

Find the 9th term in the following geometric sequence:

4, 8, 16, 32, ...

• 384

• 512

• 768

• 1,024

Multiple Choice

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

• 59,050

• -59,048

• -78,732

• 118,096

Multiple Choice

Evaluate the geometric series $$1-2+4-8,\ ...,\ \ \ \ \ \ \ n=8$$  

• $$\frac{1}{3}$$  

• -86

• -87

• -85

Multiple Choice

Evaluate the geometric series below:
4 + 20 + 100 + 500...,  S₇

• 88419

• 78124

• 91846

• 92234

Multiple Choice

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

• 44

• $$\frac{1}{3}$$  

• 43

• 49

Multiple Choice

$$Evaluate\ \ \ \ \ \sum_{i\ =1}^9-3\cdot3^{\ \left(i-1\right)}$$  

• -28,056

• -29,523

• -31,724

• -30,628

Multiple Choice

Find the sum of the infinite geometric series, if it exists. $$\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$$  

• 8

• 8/5

• 10

• Does not exist

Multiple Choice

$$\sum_{k=1}^{\infty}\left(\frac{4}{5}\right)^{k-1}$$  Find the sum of the series if it exists.

• 4/5

• 5

• 6.5

• Does not exist