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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
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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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