Multiples of 9 lying between 300 and 700 are 306, 315, 324, …, 693.

Sum of these numbers forms an arithmetic series 306 + 315 + 324 + … + 693.

Here, first term = a = 306

Common difference = d = 9

We first find the number of terms in the series.

Here, last term = l = 693

∴ 693 = a + (n - 1)d

⇒ 693 = 306 + (n - 1)9

⇒ 693 - 306 = 9n - 9

⇒ 387 = 9n - 9

⇒ 387 + 9 = 9n

⇒ 9n = 396

⇒ n = 44

Now, Sum of n terms of this arithmetic series is given by:

S_n = [2a + (n - 1)d]

Therefore sum of 44 terms of this arithmetic series is given by:

∴ S₄₄ = [2(306) + (44 - 1)(9)]

= 22 × [612 + 387]

= 22 × 999

= 21978