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Find the sum of all three-digit natural numbers which are divisible by 13.

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This is the basic and conceptual question from arithmetic progression chapter in which we have to find the sum of all three-digit natural numbers which are divisible by 13.

Book RS Aggarwal, Class 10, chapter 5C, question no 17.

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  1. 3-digit natural numbers: 100,101,102,.....,999.
    3-digit natural numbers divisible by 13:
    104,117,130,......,988
    Which is an AP.
    Here, a=104,d=13,l=988
    l=a+(n1)d
    988=104+(n1)13
    n=69
    There are 69 terms.
    Find the sum of 69 terms:
    Sn=n/2(a+l)
    =69/2(104+988)
    =37674.

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