Choose the correct answer in each of the following questions:

Question:

Choose the correct answer in each of the following questions:

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

(a) $(5-2 n)$

(b) $(6-2 n)$

(c) $(2 n-5)$

(d) $(2 n-6)$

Solution:

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

$\therefore S_{n}=5 n-n^{2}$

$\Rightarrow S_{n-1}=5(n-1)-(n-1)^{2}$

$=5 n-5-n^{2}+2 n-1$

$=7 n-n^{2}-6$

∴ nth term of the AP, an = S− S− 1

$=\left(5 n-n^{2}\right)-\left(7 n-n^{2}-6\right)$

$=6-2 n$

Thus, the nth term of the AP is (6 − 2n).

Hence, the correct answer is option B.