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Question

Find the number of terms of the AP 18, 15, 12, ... so that their sum is 45. Explain the double answer.

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Solution

Here, a = 18 and d = (15- 18) = -3
Let the required number of terms be n.
Then, Sn = 45
n2 [ 2a + n-1d] = 45
n2×2×18 + n-1×-3=45n2×39 -3n = 453n2-39n+90=0n2-13n+30=0n2-10n-3n+30=0n(n-10)-3(n-10)=0(n-10)(n-3)=0n=3 or n=10
∴ Sum of the first 3 terms = sum of the first 10 terms = 45
This means that the sum of all terms from 4th to 10th is zero.

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