The sum of all the integers which are divisible by ‘7’ and lying between 50 and 500 is

sum:56,63,70,….497
56+63+70+…+497 are in A.P.
a=56, d=7
${\text{t}}_n$=497=56+(n-1) $\left[t_n=a+\left(n-1\right)d\right]$
$\Rightarrow$n=64
$S_{64}$= 64/2[56+497]=17696  $\left[S_n=\frac{n}{2}\left(2a+\left(n-1\right)d\right) or \frac{n}{2}\left(a+l\right) \right]$