Geometric Series Formula

GEOMETRIC SERIES

GEOMETRIC SERIES

The sum of the terms in a geometric sequence.

GEOMETRIC SERIES

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

GEOMETRIC SERIES

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

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

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 Blanks

What is the sum of the first five terms of the sequence 5,15,45,...? On the problem, what is the first term?

Fill in the Blanks

What is the sum of the first five terms of the sequence 5,15,45,...? On the problem, what is the common ratio?

Fill in the Blanks

On the problem, how many terms are to be added?

Fill in the Blanks

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

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

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

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

Fill in the Blanks

What is the sum of the first six terms of the sequence 2,8,32,...? On the problem, what is the first term?

Fill in the Blanks

What is the sum of the first six terms of the sequence 2,8,32,...? On the problem, what is the common ratio?

Fill in the Blanks

On the problem, how many terms are to be added?

Fill in the Blanks

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

INFINITE GEOMETRIC SERIES

 $S_{\infty}=\frac{a_1}{1-r}$  

INFINITE GEOMETRIC SERIES

 $S_{\infty}=\frac{a_1}{1-r}$  

Multiple Choice

Find the indicated sum of the geometric sequence if its first term is 318 and the common ratio is one-half. Is the problem an example of INFINITE GEOMETRIC SERIES?

• Yes, it is!

• No, it is not!

Multiple Choice

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

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

• $$S_{\infty}=\frac{a_1}{1-r}$$

Fill in the Blanks

Find the indicated sum of the geometric sequence if its first term is 318 and the common ratio is one-half.