Question

Find the sum of all multiplies of 9 lying between 300 and 700.

Answer 1

The numbers lying between 300 and 700 which are multiples of 9 are

306, 315, 324,…, 693

a₂ – a₁ = 315 – 306 = 9

a₃ – a₂ = 324 – 315 = 9

∵ a₃ – a₂ = a₂ – a₁ = 9

Therefore, the series is in AP

Here, a = 306, d = 9 and a_n = 693

We know that,

a_n = a + (n – 1)d

⇒ 693 = 306 + (n – 1)9

⇒ 693 - 306 = (n – 1)9

⇒ 387 = (n – 1)9

⇒ 43 = (n – 1)

⇒ n = 44

Now, we have to find the sum of this AP

⇒ S₄₄ = 22[612 + 387]

⇒ S₄₄ = 22[999]

⇒ S₄₄ = 21978

Hence, the sum of all numbers lying between 300 and 700 is 21978.