Question

Find the sum of those integers between 1 and 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

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

Which form an AP with first term (a) = 10 

And common difference (d) = 20 – 10 = 10

n^th term a_n = Last term (l) = 490

∴ Sum of n terms between 1 and 500,

S_n = `n/2[a + 1]`  ...(i)

∵ a_n = a + (n – 1)d = l

⇒ 10 + (n – 1)10 = 490

⇒ (n – 1)10 = 480

⇒ n – 1 = 48

⇒ n = 49

From equation (i),

S₄₉ = `49/2(10 + 490)`

= `49/2 xx 500`

= 49 × 250

= 12250