Question

Find the sum of all natural numbers that are less then $100$ and divisible by $4$.

Answer 1

The given series will be:

$4+18+12+.......+96$

Or $4(1+2+3+.......+24)$

The series is an $AP$. So, using the formula for sum of n terms of an Arithmetic progression to find the required sum:

$S_n=\frac{n}{2}(a+a_n)$ ,

where $a$ is the first term, $a=1$

Common difference, $d=1$

Number of terms, $n=24$

$1+2+3+\cdots +24=\frac{n(n+1)}{2}=\frac{24\times 25}{2}=12\times 25=300$

$\text{Required Sum}=4\left(300\right)=1200$