# if the first term of Ap is 22 and n th term is -11 and the sum of first term is 66 find n and d?

AP..........

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- BrianLv 77 years agoFavorite Answer
The sum of the first n terms of an AP is S(n) = (n/2)*(a(1) + a(n)).

We are given that S(n) = 66, a(1) = 22 and a(n) = -11, so

66 = (n/2)*(22 + (-11)) = (n/2)*(11) ----> n/2 = 6 ----> n = 12.

Now, for an AP the nth term is a(n) = a(1) + (n - 1)*d, so

-11 = 22 + (12 - 1)*d ----> -33 = 11*d ----> d = -3.

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