Question

Find the sum of all odd natural numbers from 1 to 150.

• A. 5625
• B. 5635
• C. 5645
• D. 5655

Answer 1

The correct option is A 5625

Clearly, the odd natural numbers from $1$ to $150$ are $1,3,5,...,149$.

This is an AP with first term $a=1$, common difference $d=2$ and last term $a_n=l=149$.

Let there be $n$ terms in this AP.

Then,

$a_n=149$

$\Rightarrow a_n=a+(n-1)d$

$149=1+(n-1)\times 2$

$149=1+2n-2$

$2n=150$

$\therefore n=75$

$\therefore$ required sum $=S_n=\frac{n}{2}[a+l]=\frac{75}{2}[1+149]=5625$