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

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An important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2012 in which we are to find the sum of all natural numbers between 200 and 400 which are divisible by 7.

Book RS Aggarwal, Class 10, chapter 5C, question no 13.

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## 203,210,217,.....,399

The abve series forms A.P. with first termÂ 203Â and common differenceÂ 7.
Also,
Last termÂ =399
Now,
anâ€‹=a+(nâˆ’1)d
399=203+(nâˆ’1)7
â‡’nâˆ’1=7399âˆ’203â€‹
â‡’n=28+1=29
Therefore,
Snâ€‹=n/2â€‹(a+l)
â‡’S29â€‹=29/2â€‹(29+399)
â‡’S29â€‹=29â€‹/2Ã—328
Â  Â  Â  Â  Â  =29Ã—164
Â  Â  Â  Â  Â  =4756

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