Question

If sum to $n$ terms of an $A.P$. is $5n^2+6n$ and $r^{th}$ term is $401$, then the value of $r$ is

• A. $40$
• B. $30$
• C. $20$
• D. $10$

Answer 1

Answer: (A)

$T_n=S_n-S_{n-1}$
i.e., $T_n=5n^2+6n-5{\left(n-1\right)}^2-6\left(n-1\right)$
$=10n+1$
$\therefore T_r=10r+1=401$
$\Rightarrow 10r=400$
$\Rightarrow r=40$