Geometric Series and Summation

GEOMETRIC SERIES

​

GEOMETRIC SERIES

The sum of the terms in a geometric sequence.

GEOMETRIC SERIES

GEOMETRIC SERIES

Multiple Choice

Is the sequence 5,15,45,... a geometric sequence?

• Yes, it is a geometric sequence with r=3.

• No, it is not a geometric sequence.

Multiple Choice

Is the sequence 2,8,32,... a geometric sequence?

• Yes, it is a geometric sequence with r=4.

• No, it is not a geometric sequence.

Multiple Choice

What is the formula to be used in finding the sum of the  first five terms of the sequence 5,15,45,...?

• $$S_n=\frac{n}{2}\left(a_1+a_n\right)$$

• $$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$$

Fill in the Blank

What is the sum of the first five terms of the sequence 5,15,45,...?

Fill in the Blank

What is the sum of the first six terms of the sequence 2,8,32,...?

Multiple Choice

Find the 8th term.

-4, 12, -36, 108

• 8748

• -1/6561

• -2916

• -729

Multiple Choice

Evaluate the geometric series below:
4 - 8 - 16 - 32...,  S₇

• 195

• 172

• 202

• 145

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

Find the sum for the following series. 

• 44

• -162

• -682

• 324

Multiple Choice

Find the geometric sum 

• -1456

• -4095

• 1456

• 4095

INFINITE GEOMETRIC SERIES

INFINITE GEOMETRIC SERIES

Multiple Choice

Evaluate the infinite geometric series:

1 + 1/5 + 1/25 + ...

• 5/4

• 9/5

• 5/6

• 65/27

Multiple Choice

Evaluate the infinite geometric series:

3 - 2 + 4/3 - 8/9 + ...

• 5/4

• 9/5

• 5/6

• 65/27

Multiple Choice

What is the formula to be used to solve the problem?

• $$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$$

• $$S_{\infty}=\frac{a_1}{1-r}$$

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

• 4/5

• 5

• 6.5

• Does not exist