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

The sum of all multiples of 9 lying between 300 and 700 is 306 + 315 + ….. + 693.

The above series is an A.P. with a = 306, d = 9 and l = 693.

Let 693 be nth term of the series then,

⇒ 693 = 306 + 9(n - 1)
⇒ 693 - 306 = 9n - 9
⇒ 387 = 9n - 9
⇒ 9n = 387 + 9
⇒ 9n = 396
⇒ n = 44.

By formula S_n = $\dfrac{n}{2}[2a + (n - 1)d]$

⇒ S₄₄ = $\dfrac{44}{2}[2 \times 306 + 9(44 - 1)]$
⇒ S₄₄ = 22[612 + 387]
⇒ S₄₄ = 22 × 999
⇒ S₄₄ = 21978.

Hence, the sum of all multiples of 9 lying between 300 and 700 is 21978.