Madhya Pradesh Police Exam Model Paper 6

Given -
sum of all integers between 81 and 719
Formula used -
sum of n - number $=\left(\mathit{n}/2\right)2\mathit{a}+\left(\mathit{n}-1\right)\times \mathit{d}$
sum of n- numbers if first and last term are given -
$\left(\mathit{n}/2\right)$ {a + l}
For nth term -
$\mathit{T}\mathit{n}=\mathit{a}+\left(\mathit{n}-1\right)\times \mathit{d}$
Solution -
Let the sum be S.
⇒ integers between 81 and 719 which is divisible by 5 .
⇒ (85, 90, 95, 100, ......................................... 715)
$\Rightarrow 715=85+\left(\mathit{n}-1\right)\times 5$
$\Rightarrow 5\times \left(\mathit{n}-1\right)=630$
$\Rightarrow \left(\mathit{n}-1\right)=126$
$\Rightarrow \mathit{n}=127$
$\Rightarrow \mathit{S}=\left(127/2\right)\times \left(85+715\right)$
$\Rightarrow \mathit{S}=\left(127/2\right)\times 800$
$\Rightarrow \mathit{S}=50,800$
∴ the sum of the integer between 81 and 719 which is divisible by 5 = 50,800.