Question

What is the sum of first $37$ odd natural numbers?

Answer 1

$\Rightarrow 1,3,5,...\dots \dots ...2n+1$

$\therefore$ ${37}^{th}$ terms $=2(n-1)+1$

$=2\left(36\right)+1=73$

$\Rightarrow 1,3,5,7,...\dots .,73$.

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

$=\frac{37}{2}(2\times 1+(37-1\left)2\right)$

$=\frac{37}{2}[2+72]$

$\Rightarrow 37\times \frac{74}{2}$

$\Rightarrow {37}^2$

$=1369$.