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, $d=11-7=4$
$a_{n}=a+(n-1) d$
$=7+(n-1) 4$
$=4 n+3$