Find the sum of all integers between 84 and 719,

Question:

Find the sum of all integers between 84 and 719, which are multiples of 5.

Solution:

The integers between 84 and 719, which are multiples of 5 are:

85, 90...715

Here, we have:

$a=85$

$d=5$

$a_{n}=715$

$\Rightarrow 85+(n-1) 5=715$

$\Rightarrow 5 n-5=630$

$\Rightarrow n=127$

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

$\Rightarrow S_{127}=\frac{127}{2}[2 \times 85+(127-1) 5]$

$\Rightarrow S_{127}=\frac{127}{2}[800]=50800$