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 (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 (8− 2).

Hence, the correct answer is option C.

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