Question

If sum of $n$ terms of an A.P. is $3 n ^ { 2 } + 5 n$ and $T _ { m } = 164$ then $m =$

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

Answer 1

Answer: (B)

27

Answer 2

Obviously

$164 = \left( 3 m ^ { 2 } + 5 m \right) - \left\{ 3 ( m - 1 ) ^ { 2 } + 5 ( m - 1 ) \right\}$

$= \left( 3 m ^ { 2 } + 5 m \right) - 3 m ^ { 2 } + 6 m - 3 - 5 m + 5$

$\Rightarrow$ $164 = 6 m + 2$ $\Rightarrow$ $m = 27$ .