Q. 265.0( 1 Vote )

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

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 an = 693

We know that,

an = 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

S44 = 21978

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

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