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 = Sn − Sn − 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.