# If the sum of n terms of an A.P.,

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, $a_{n}=164$

$\Rightarrow a+(n-1) d=164$

$\Rightarrow 8+(n-1) 6=164$

$\Rightarrow n=27$