This is the basic and conceptual question from arithmetic progression chapter in which we are to calculate the sum of all multiples of 9 lying between 300 and 700.
Book – RS Aggarwal, Class 10, chapter 5C, question no 16.
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Clearly, the numbers between 300 and 700 which are multiples of 9 are 306,315,324,...,693.
This is an AP with first term a=306, common difference d=9 and last term l=693.
Let there be n terms in this AP. Then,
an=693⇒a+(n−1)d
693⇒306+(n−1)×9
∴n=44
∴ Required sum =Sn=n/2[a+l]
=244[306+693]
=21978