Question

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

Answer 1

LCM of 2 and 5 = 10

so the numbers would be: 10,20,30,40......490

A.P = aₓ = a+(n-1)d

a (first number) = 10

d(difference) = 20-10 =10

aₓ(last term) = 490

490 = 10+(n-1)10

480 = (n-1)10

48 = n-1

49 = n

Now the sum of the terms:

S₄₉ = n/2(a+aₓ)

= 49/2(10+490)

= 49/2 *500

= 49*250

= 12250