SOLUTION: how many terms of the series -9,-6,-3, ....will be 66?

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Question 1091788: how many terms of the series -9,-6,-3, ....will be 66?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you mean they will sum to 66.
a%5B1%5D=-9
d=-6-%28-9%29=-6%2B9=3
So then,
S%5Bn%5D=%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29
66=%28n%2F2%29%282%28-9%29%2B%28n-1%29%283%29%29
n%28-18%2B3n-3%29=132
n%283n-21%29=132
n%28n-7%29=44
n%5E2-7n-44=0
%28n-11%29%28n%2B4%29=0
n must be a positive integer so,
n-11=0
n=11