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

Since, multiples of 2 as well as of 5 = LCM of (2, 5) = 10

Multiples of 2 as well as of 5 between 1 and 500 is 10, 20, 30, …., 490.

Clearly this is an AP with common difference, d = 10

And first term, a = 10

Let the no if terms in this AP are n

Then, by nth term formula

a_n = a + (n - 1)d

490 = 10 + (n - 1)10

480 = (n - 1)10

n - 1 = 48

n = 49

now, Sum of this AP

[ as last term is given]

= 49(250)

= 12250