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Q.

The sum of the integers between 100 and 200 that are divisible by 9 is[[1]].


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Detailed Solution

The sum of the integers between 100 and 200 that are divisible by 9 is 1683.
Given, AP series are the integers between 100 and 200 that are divisible by 9.
The integers are 108,117,126.....198.
So,108 = a, 9 = d and 198 = a n   a n = a+ n−1 d  
198=108+ n−1 9 n−1 9=90 n−1=10 n=11  .
Now, for the sum of the nth terms,
Using, 108 = a, 9 = d and 198 = a n   in the formula,
S n = n 2 2a+ n−1 d    S 11 = 11 2 2 108 + 11−1 9 S 11 = 11 2 216+90 S 11 = 11 2 306 S 11 =1683  .
So, their sum is 1683.
Thus, the final answer is 1683.
 
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