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 between 1 and 500 which are multiples of 2 as well as of 5 i.e. which are multiples of 10 are $10,20,30,...,490$.

This is an AP with first term $a=10$, common difference $d=10$ and last term $l=490$.

Let there be n terms in this AP. Then,

$a_n=490\Rightarrow a+(n-1)d=490\Rightarrow 10+(n-1)\times 10=490$

$\Rightarrow (n-1)10=480\Rightarrow n-1=48\Rightarrow n=49$

$\therefore Requiredsum=S_n=\frac{n}{2}[a+l]=\frac{49}{2}[10+490]=12250$