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Question

Find the sum of all the numbers between 100 and 200 which are divisible by 7.

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Solution

The numbers which are divisible by 7 between 100 and 200 are 105,112,119,126,...,196

The given series is in A.P. Since, the difference between the consecutive terms is constant. i.e., 11105=119112=...=7

The first term a=105

The common difference d=7

The last term an=196

a+(n1)d=196

105+(n1)7=196

(n1)7=91

n1=13

n=14

Therefore the sum the terms is Sn=n2(a+an)

Sn=142(105+196)

Sn=7(301)=2107

Therefore, the sum of all the numbers between 100 and 200 which are divisible by 7 is 2107

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