SOLUTION: the 1st term of A.P is -12 and last term is 40. if the sum of the series is 196,find the number of terms and the common difference.

Question 1035723: the 1st term of A.P is -12 and last term is 40. if the sum of the series is 196,find the number of terms and the common difference.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
x1 = -12
:
1) 40 = -12 + d(n-1), where n is the nth term and d is the common difference
:
2) 196 = (n/2) * ( 2*(-12) + (n-1)*d)
:
solve equation 1 for d and substitute in equation 2
:
d = 52 / (n-1)
:
196 = (n/2) * (2*(-12) + (n-1)*52/(n-1))
:
196 = (n/2) * (-24 + 52)
:
196 = 14n
:
n = 14
:
substitute in equation 1 to find d
:
40 = -12 + d * (14 -1)
:
13d = 52
:
d = 4
:
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the number of terms is 14
the common difference is 4
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:
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