# How do you write a rule for the nth term of the arithmetic sequence and then find #a_22# given #45, 31, 17, 3,...#?

##### 1 Answer

Sep 22, 2017

#### Explanation:

First, we figure out the sequence. Then we generalize it.

This one shows a decrease of 14 (-14) between every value in the series.

So, if we start with

The next one would be

Recognizing that now our multiplier is the same as our sequence identifier (2) we can generalize the expression to:

NOW putting in our values for