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#?

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Answer 1 · 2017-05-30T02:30:54

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

#a_22 = 0#

First, find #a_1#:

#a_1 = a_13 - 12d#

#a_1 = 99 - 12(-11)#

#a_1 = 99 + 132 = 231#

Now use the formula #a_n = a_1 + d(n-1)#

The rule for the nth term is #a_n = 231 - 11(n-1)#

Finally, plug in #n=22# and solve.

#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