# Find the sum of all integers between 50 and 500 which are divisible by 7.

Question:

Find the sum of all integers between 50 and 500 which are divisible by 7.

Solution:

The integers between 50 and 500 that are divisible by 7 are:

56, 63...497

Here, we have:

$a=56$

$d=7$

$a_{n}=497$

$\Rightarrow 56+(n-1) 7=497$

$\Rightarrow 7 n-7=441$

$\Rightarrow 7 n=448$

$\Rightarrow n=64$

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$\Rightarrow S_{64}=\frac{64}{2}[2 \times 56+(64-1) 7]$

$\Rightarrow S_{64}=32[2 \times 56+63 \times 7]=17696$