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Question

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

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Solution

Clearly, the numbers between 1 and 500 which are multiples of 2 as well as of 5 i.e. which are multiples of 10 are 10,20,30,...,490.

This is an AP with first term a=10, common difference d=10 and last term l=490.

Let there be n terms in this AP. Then,

an=490a+(n1)d=49010+(n1)×10=490

(n1)10=480n1=48n=49

Required sum=Sn=n2[a+l]=492[10+490]=12250

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