Question

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

Answer 1

The numbers lying between $200$ and $400$ which are divisible by $7$ are $203,210,217,...399$
$\therefore$ First term, $a=203$
Last term, $a_n=399$ & Common difference, $d=7$
Let the number of terms of the A.P. be $n$.
$\therefore a_n=399=a+(n-1)d\Rightarrow 399=203+(n-1)7\Rightarrow 7(n-1)=196\Rightarrow n-1=28\Rightarrow n=29\therefore S_{29}=\frac{29}{2}(203+399)=\frac{29}{2}\left(602\right)=\left(29\right)\left(301\right)=8729$
Thus, the required sum is $8729$