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,...?

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

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

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,...?

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

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

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?

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

• $$S_{\infty}=\frac{a_1}{1-r}$$