If the sum of n terms of an A.P.
Question:

If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is

(a) 4n − 3

(b) 3 n − 4

(c) 4 n + 3

(d) 3 n + 4

Solution:

(c) 4 n + 3

$S_{n}=2 n^{2}+5 n$

$S_{1}=2 \cdot 1^{2}+5 \cdot 1=7$

$\therefore a_{1}=7$

$S_{n}=2 \cdot 2^{2}+5 \cdot 2=18$

$\therefore a_{1}+a_{2}=18$

$\Rightarrow a_{2}=11$

Common difference, $d=11-7=4$

$a_{n}=a+(n-1) d$

$=7+(n-1) 4$

$=4 n+3$

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