# How do you write a rule for the nth term of the arithmetic sequence and then find #a_22# given #d=-11, a_13=99#?

##### 1 Answer

May 30, 2017

#### Explanation:

First, find

#a_1 = a_13 - 12d#

#a_1 = 99 - 12(-11)#

#a_1 = 99 + 132 = 231#

Now use the formula

The rule for the nth term is

#a_n = 231 - 11(n-1)#

Finally, plug in

#a_n = 231-11(n-1)#

#a_22 = 231 - 11(22-1)#

#a_22 = 231 - 11(21)#

#a_22 = 231 - 231#

#a_22 = 0#

*Final Answer*