Question

Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.

Answer 1

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

But multiples of 2 as well as 5 from 1 to 500 is 10, 20, 30,..., 500.

∴ a = 10, d = 10, a_n = l = 500

∵ a_n = a + (n – 1)d = l

⇒ 500 = 10 + (n – 1)10

⇒ 490 = (n – 1)10

⇒ n – 1 = 49

⇒ n = 50

∵ S_n = ${\displaystyle \frac{n}{2}(a+l)}$

⇒ S₅₀ = ${\displaystyle \frac{50}{2}(10+500)}$

= ${\displaystyle \frac{50}{2}\times 510}$

=  50 × 255

= 12750