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

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:

Sn = [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

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