Ask a Teacher

Search



find the sum of all odd integers between 2 and 100 divisible by 3.
The number should be odd as well as divisible by 3. The series would be 3, 9 , 15 , 21 , -------- 99.
Here a = 3 ,d = 6 and nth term = 99.
First find out how many terms would be there and then we would calculate the sum of the first n terms.
Now nth term = a+(n-1)*d
or 99 = 3+(n-1)*6
or 99 = 3+6n-6
or 102 = 6n
or n = 17
Now sum of first 17 terms of this series = n/2[2a+(n-1)*d]
or 17/2[2*3+(17-1)*6]
or 17/2[6+(16)*6]
or 17/2[6+96]
or 17/2[102]
or 17*51 = 867
So the answer is 867.


comments powered by Disqus