Q. 7

The sum of first n terms of an AP is (5n – n2). The nth term of the AP is
A. (5 – 2n)

B. (6 – 2n)

C. (2n – 5)

D. (2n – 6)

Answer :

Let Sn denotes the sum of first n terms of an AP.


Sum of first n terms = Sn = 5n - n2


Then nth term is given by: an = Sn - Sn - 1


an = (5n - n2) - [5(n - 1) - (n - 1)2]


= (5n - n2) - [5n - 5 - (n2 + 1 - 2n)]


= 5n - n2 - 5n + 5 + n2 + 1 - 2n


= 6 - 2n

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