Question

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

Answer 1

Natural numbers between $200$ and $400$ divisible by $7$-

$203,210,217,.....,399$

The abve series forms A.P. with first term $203$ and common difference $7$.

Also,

Last term $=399$

Now,

$a_n=a+(n-1)d$

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

$\Rightarrow n-1=\frac{399-203}{7}$

$\Rightarrow n=28+1=29$

Therefore,

$S_n=\frac{n}{2}(a+l)$

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

$\Rightarrow S_{29}=\frac{29}{2}\times 328=29\times 164=4756$