Question

Find the sum of all natural numbers between 200 and 300 which are exactly divisible by 6.

Answer 1

The arithmetic series is, 204 + 210 + 216 + ...... + 294
$\therefore a=204,d=210-204=6,T_n=294,S_n=?$
To find $S_n$, we should first find the value of 'n'
$T_n=294$
$a+(n-1)d=294$
$204+(n-1)6=294$
$204+6n-6=294$
$198+6n=294$
$6n=294-198=96$
$\therefore n=16$
$S_n=\frac{n}{2}[a+T_n]$
$S_{16}=\frac{16}{2}[204+294]=\frac{16}{2}\times 498=3984$