Question

The $n^{th}$ term of the series $4+14+30+52+80+114+.....$ is

• A. 5n-1
• B. $2n^2+2n$
• C. $3n^2+n$
• D. $2n^2+2$

Answer 1

The correct option is C $3n^2+n$

Let nth term of the series is $T_n$ and $S_n=4+14+30+52+80+114+----+T_n..$(i)

$T_n=4+\frac{n-1}{2}\left[\right(2\times 10)+(n-2\left)6\right]$

$T_n=4+\frac{n-1}{2}\left[\right(20)+6n-12]$

$T_n=4+\frac{n-1}{2}\left[2\right(3n+4\left)\right]$
$T_n=3n^2+n$