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


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.


(b) 27th

$S_{n}=3 n^{2}+5 n$


$\therefore a_{1}=8$


$\therefore a_{1}+a_{2}=22$

$\Rightarrow a_{2}=14$

Common difference, $d=14-8=6$

Also, $a_{n}=164$

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

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

$\Rightarrow n=27$






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