Question

What is the sum of all natural numbers between $200$ and $400$ which are divisible by $7$?

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

Answer 1

The correct option is C $8729$

The numbers lying between $200$ and $400$, which are divisible by $7$ are-

$203,210,217,­­­­­­­­\dots 399$

Therefore,

First term $\left(a\right)=203$

Last term $\left(l\right)=399$

Common difference $\left(d\right)=7$

Let the number of terms of the A.P. be $n$.

$\therefore a_n=399$

$\Rightarrow 399=a+(n-1)d$

$\Rightarrow 399=203+(n-1)7$

$\Rightarrow 7(n-1)=196$

$\Rightarrow n-1=28$

$\Rightarrow n=29$

$S_{29}$ $=\frac{29}{2}(203+399)=8729$