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find the sum of all integers between 100 and 300 which are divisible by 7

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Qazwead asked in Math

Find the sum of all the integers between 100 and 200 that are not divisible by 9

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Abhishek Jha answered this
4374 helpful votes in Math, Class IX

Sum of integers between 100 and 200 that are divisible by 9 =  108 + 117 + 126 + … + 198
Here this is the sequence of an A.P. where first term;a = 108, common difference;d = 9
Here nth term of an A.P. is 198, so we have;

So sum of 11 terms is given by;
 108 + 117 + 126 + … + 198 = 
So the sum of integers between 100 and 200 which are divisible by 9 is 1683.

The sum of the integers between 100 and 200 which are not divisible by 9
= The sum of all integers between 100 and 200 – The sum of the integers between 100 and 200 which are divisible by 9

Therefore the sum of the integers between 100 and 200 which are not divisible by 9 is 13167.