Question

The sum of integers between. 1 abd 500 which are multiples of 2 as well as 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⇒a+(n−1)d=490⇒10+(n−1)×10=490

⇒(n−1)10=480⇒n−1=48⇒n=49

∴Required sum=S

n

=

2

n

[a+l]=

2

49

[10+490]=12250