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**If the sum of it terms of an A.P. is 2$\mathbf{n}^{2}$ + 5n, then its nth term is**

A. 4n – 3
B. 3n – 4
C. 4n + 3
D. 3n + 4
**Answer: Option C**

## Show Answer

Solution(By Apex Team)

Let a be the first term and d be the common difference of an A.P. and
$\begin{aligned}S_n&=2n^2+5n\\
\therefore S_1&=2(1)^2+5\times1\\
&\quad=2+5\\
&\quad=7\\
\therefore S_2&=2(2)^2+5\times2\\
&\quad=8+10\\
&\quad=18\\
\therefore\text{ First term }\left(a_1\right)&=7\text{ and }\\
\text{ Second term }a_2&=S_2-S_1\\
&\quad=18-7\\
&\quad=11\\
\therefore d&=a_2-d_1\\
&=11-7\\
&=4\\
\text{ Now }a_n&=a+(n-1)d\\
&\quad=7+(n-1)4\\
&\quad=7+4n-4\\
&=4n+3\end{aligned}$

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