Question

The $n^{th}$ terms of the series $3+7+13+21+\dots$ is

• A. $4n-1$
• B. $n^n+2n$
  
• C. $n^2+n+1$
• D. $n^2+2$

Answer 1

The correct option is C $n^2+n+1$

$S=3+7+13+21+....t\left(n\right)\to \left(1\right)$
$S=3+7+13+.....t(n-1)+t\left(n\right)\to \left(2\right)$
Subtracting $\left(2\right)$ from $\left(1\right)$
$t\left(n\right)=3+4+6+8+12+.......2nt\left(n\right)=1+2+4+6+8+.......+20=1+2\times \frac{n(n+1)}{2}=1+n+n^2$