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

Options

A. 6729
B. 8712
C. 8729
D. 9276

Answer

C

Explanation

The numbers between 200 and 400 which are divisible by 7, are
`203,210,217,……,399`
This is an A.P with first term = a = 203 and common difference = d = 7
Now, let number of terms be n.
Therefore from the `n^(th)` term of `A.P=a+(n-1)d` we have
`399=203+(n-1)7`
`implies(196)/(7)=(n-1)impliesn=29`
Required sum `=(n)/(2)[a+l]"where "l="last term"`
Thus, required sum `=(29)/(2)[203+399]`
`=(29xx602)/(2)=8729`