SOLUTION: 15+12+9+6...=-90 find number of terms

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Question 1040203: 15+12+9+6...=-90 find number of terms
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D=15
d=-3
S%5BN%5D=-90
So in terms of a%5B1%5D and d, the sum is,
S%5BN%5D=N%2Aa%5B1%5D%2B%28%28N%28N%2B1%29%29%2F2%29%2Ad
Substituting,
-90=N%2A15%2B%28%28N%28N%2B1%29%29%2F2%29%2A%28-3%29
-90=15N-%283%2F2%29%28N%28N%2B1%29%29
-180=15N-3%28N%5E2%2BN%29
-60=5N-%28N%5E2%2BN%29
N%5E2-4N-60=0
%28N-10%29%28N%2B6%29=0
Only the positive value makes sense in this problem.
N-10=0
N=10