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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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+(n−1)d
988=104+(n−1)13
n=69
There are 69 terms.
Find the sum of 69 terms:
Sn=n/2(a+l)
=69/2(104+988)
=37674.