Question

$3+5+7+.......ToNTerm$

Answer 1

$S_n=3+5+7+.......+n$

Since above series is an AP with $a=3$

$d=5–3=2$

Therefore,

$\begin{array}{rcl}{S}_n& =& \frac{n}{2}\left[2a+(n-1)d\right]\\ & =& \frac{n}{2}\left[2\times 3+(n-1)2\right]\\ & =& \frac{n}{2}\left[6+2n-2\right]\\ & =& \frac{n}{2}\left[2n+4\right]\\ & =& \frac{n}{\sout{2}}\times \sout{2}\left[n+2\right]\\ & =& n(n+2)\end{array}$

Hence, the required answer is $\begin{array}{rcl}& & n(n+2)\end{array}$.