Question:
Choose the correct answer in each of the following questions:
The sum of first n terms of an AP is (4n2 + 2n). The nth term of the AP is
(a) $(6 n-2)$
(b) $(7 n-3)$
(c) $(8 n-2)$
(d) $(8 n+2)$
Solution:
Let Sn denotes the sum of first n terms of the AP.
$\therefore S_{n}=4 n^{2}+2 n$
$\Rightarrow S_{n-1}=4(n-1)^{2}+2(n-1)$
$=4\left(n^{2}-2 n+1\right)+2(n-1)$
$=4 n^{2}-6 n+2$
$\therefore n^{\text {th }}$ term of the $\mathrm{AP}, a_{n}=S_{n}-S_{n-1}$
$=\left(4 n^{2}+2 n\right)-\left(4 n^{2}-6 n+2\right)$
$=8 n-2$
Thus, the nth term of the AP is (8n − 2).
Hence, the correct answer is option C.