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Question

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Solution
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The numbers lying between 200 and 400 which are divisible by 7 are 203,210,217,...399
First term, a=203
Last term, an=399 & Common difference, d=7
Let the number of terms of the A.P. be n.
an=399=a+(n1)d399=203+(n1)77(n1)=196n1=28n=29S29=292(203+399)=292(602)=(29)(301)=8729
Thus, the required sum is 8729

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