Question:
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
(a) 26th
(b) 27th
(c) 28th
(d) none of these.
Solution:
(b) 27th
$S_{n}=3 n^{2}+5 n$
$S_{1}=3(1)^{2}+5(1)=8$
$\therefore a_{1}=8$
$S_{2}=3(2)^{2}+5(2)=22$
$\therefore a_{1}+a_{2}=22$
$\Rightarrow a_{2}=14$
Common difference, $d=14-8=6$
Also, $a_{n}=164$
$\Rightarrow a+(n-1) d=164$
$\Rightarrow 8+(n-1) 6=164$
$\Rightarrow n=27$