Question

Find the sum of all integers from 1 to 500 which are multiples of 2 or 5

Answer 1

Fact : The multiples of 2 and 5 are also the multiples of 10

So now we know it forms an AP

10 ,20, 30..........490   (i am assuming 500 is not included in this series)

First term = a = 10

last term = l = 490

difference = d = 10

We know that

An =  a + (n - 1)d

Or

l = a + (n - 1)d

490 = 10 + (n - 1)10

49 = n

So there are total 49 terms in between 1 and 500 which are multiples of 2 and 5

Now ,we know that

Sn = n/2 ( a + l)

      49/2 (10 + 490)

= 12250

The answer may vary if 500 is included in the series