Question

Find the sum of all numbers between $100$ and $200$ which are not divisible by $5$

Answer 1

We need to find the sum of numbers between $100$ and $200$ which are not divisible by $5$.

We can first find the sum of all numbers between $100$ and $200$, then later subtract the sum of numbers divisible by $5$.

Let $S$ be sum of numbers between $100$ and $200$.

$S=\frac{200\times 201}{2}-\frac{100\times 101}{2}$ {Using the formula sum of series $1,2,3,...,n$ is $\frac{n(n+1)}{2}$}

$\Rightarrow S=15050$

Let $s$ be sum of numbers between $100$ and $200$ which are divisible by $5$.

$s=\frac{20}{2}(2\times 105+(20-1)\times 5)=3050$

The required sum $=S-s=15050-3050=12000$