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.
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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
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1) 40 = -12 + d(n-1), where n is the nth term and d is the common difference
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2) 196 = (n/2) * ( 2*(-12) + (n-1)*d)
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solve equation 1 for d and substitute in equation 2
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d = 52 / (n-1)
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196 = (n/2) * (2*(-12) + (n-1)*52/(n-1))
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196 = (n/2) * (-24 + 52)
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196 = 14n
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n = 14
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substitute in equation 1 to find d
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40 = -12 + d * (14 -1)
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13d = 52
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d = 4
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the number of terms is 14
the common difference is 4
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