Question

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

Answer 1

Same as part (i)

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 = 1

⇒ 500 = 10 + (n – 1)10

⇒ 490 = (n – 1) 10

⇒ n – 1 = 49

⇒ n = 50

∵ `S_n = n/2(a + 1)`

⇒ `S_50 = 50/2(10 + 500) = 50/2 xx 510`

=  50 × 255

= 12750