Question

If the sum of n terms of an A.P. is $3n^2+5n$ and its mth term is 164, find the value of m.

• A. $25$
• B. $27$
• C. $29$
• D. none of these

Answer 1

The correct option is B $27$

Let $S_n$ denote the sum of n terms and $a_n$ be the nth term of the given AP. Then,

$S_n=3n^2+5n$

$S_{n-1}=3(n-1{)}^2+5(n-1)=3n^2-n-2$

Now, $a_n=S_n-S_{n-1}$

$a_n=(3n^2+5n)-(3n^2-n-2)$

$a_n=6n+2$

Now, $a_m=164$

$6m+2=164$

$6m=162$

$m=27$