Question 1109670: The number of terms in an A.P. whose first term is 5, common difference 3, and sum 55 is
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! the formula for the sum of the first n terms of a arithmetic progression(AP) when we do not know the nth term is
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s(n) = (n/2) * (2 * a(0) + (n-1) * d), where a(0) is the first term and d is the common difference
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we are given
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(1) 55 = (n/2) * (2*5 + 3*(n-1))
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solve for n
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55 = (n/2) * (10 + 3n - 3)
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110 = n * (7 + 3n)
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3n^2 +7n -110 = 0
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(3n+22) * (n-5) = 0
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n = -22/7 and n = 5
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we reject the negative value for n
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there are 5 terms, namely
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5, 8, 11, 14 , 17
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to check this we use the formula
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55 = (5/2) * (2 * 5 + 3 * (5 - 1)
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55 = (5/2) * 22 = 55
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our answer checks
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