SOLUTION: the 10th term of an A.P is-27 and the 5th term is -12, what is the 18th term?

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Question 1052540: the 10th term of an A.P is-27 and the 5th term is -12, what is the 18th term?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B10%5D=a%5B1%5D%2B%2810-1%29%2Ad=-27
1.a%5B1%5D%2B9d=-27
and
a%5B5%5D=a%5B1%5D%2B%285-1%29%2Ad=-12
2.a%5B1%5D%2B4d=-12
Subtracting 2 from 1,
a%5B1%5D%2B9d-a%5B1%5D-4d=-27-%28-12%29
5d=-15
d=-3
Then,
a%5B1%5D%2B4%28-3%29=-12
a%5B1%5D=0
So then,
a%5B18%5D=a%5B1%5D%2B%2818-1%29%2Ad
a%5B18%5D=0%2B17%28-3%29
a%5B18%5D=-51