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

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.

• 42

1st find the sum all integers divisible by 9 then find sum of all integers b/w 100 200 then sub sum of all integers divisible by 9 from the sum all integers b/w 100 200

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