Question

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

Answer 1

Clearly, the numbers from 1 to 500 which are multiples of 2 as well as of 5 i.e. which are multiples of 10 are $10,20,30,...,500$.

This is an AP with first term $a=10$, common difference $d=10$ and last term $l=500$.

Let there be n terms in this AP. Then,

$a_n=500\Rightarrow a+(n-1)d=500\Rightarrow 10+(n-1)\times 10=500\Rightarrow n=50$

$\therefore$ Required sum $=S_n=\frac{n}{2}[a+l]=\frac{50}{2}[10+500]=12750$