Question

If the sum of n terms of an A.P., if $3n^2+5n$ then which of its terms is 164 ?

• A. 26th
• B. 27th
• C. 28th
• D. None of these

Answer 1

The correct option is B

27th

$S_n=3n^2+5n$

$S_1=3(1{)}^2+5(1)=8$

$\therefore a_1=8$

$S_2=3(2{)}^2+5(2)=22$

$\Rightarrow a_2=14$

Common difference, d = 14 - 8 = 6

Also, $a_n=164$

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

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

$\Rightarrow n=27$