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

Given:

Integers between 84 and 719, which are multiples of 5.

To do:

We have to find the sum of all integers between 84 and 719, which are multiples of 5.

Solution:

Integers between 84 and 719, which are multiples of 5 are \( 85,90,95, \ldots, 715 \).

The sequence is in A.P.

Here,

\( a=85 \) and \( d=90-85=5 \) \( l=715 \)

We know that,

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

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

$\Rightarrow 715=85+5n-5$

$\Rightarrow 715-80=5 n$

$\Rightarrow n=\frac{635}{5}=127$

$\therefore n=127$

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

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

$=\frac{127}{2}[170+126 \times 5]$

$=\frac{127}{2}(800)$

$=127 \times 400$

$=50800$

The sum of all integers between 84 and 719 which are multiples of 5 is $50800$.