Question

Find the sum of $5+7+9+11+13+....$ for $50$ terms.

Answer 1

Consider the given series.

$5+7+9+11+13+....$

SO, $a=5,n=50,d=2$

We know that the sum of the $n$ terms

$S=\frac{n}{2}[2a+(n-1\left)d\right]$

So,

$S=\frac{50}{2}[2\times 5+(50-1)\times 2]$

$S=25[10+49\times 2]$

$S=25[10+98]$

$S=25\left[108\right]$

$S=2700$

Hence, this is the answer.