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:
$a=85$
$d=5$
$a_{n}=715$
$\Rightarrow 85+(n-1) 5=715$
$\Rightarrow 5 n-5=630$
$\Rightarrow n=127$
$S_{n}=\frac{n}{2}[2 a+(n-1) d]$
$\Rightarrow S_{127}=\frac{127}{2}[2 \times 85+(127-1) 5]$
$\Rightarrow S_{127}=\frac{127}{2}[800]=50800$