We have asked to find the sum of all the multiples of 9 lying between 300 and 700.

Sir please give me a detailed solution of this question as it is very important for examination

ML Aggarwal Avichal Publication Arithmetic Progression chapter 9 question no 20 iii

Multiples of 9 lying between 300 and 700=306,315,324,333,......,693

Here, a=306,d=9 and l=693

We know that, l=a+(n−1)d

693=306+(n−1)×9

(n−1)×9=693−306=387

n−1=9387=43

n=43+1=44

There are 44 terms.

Find the sum of 44 terms:

S44=2n[a+l]

=244[306+693]

=22×999=21978.