Question

The sum all positive integral multiples of 5 less than 100 is

Answer 1

The sum of the positive integral multiples of 5 less than 100 is 950

Explanation:

To find the sum of all positive integral multiples of 5 less than 100.

The multiples of 5 less than 100 is given by

5, 10, 15, 20, ..........., 95

The sum of all the terms can be determined using the formula,

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

where n can be determined using the formula,

$n=\frac{\text {Last Term-First Term}}{\text {Differemce}}+1$

$n=\frac{95-5}{5}+1$

$n=\frac{90}{5}+1$

$n=18+1$

$n=19$

Substituting the values $n=19$ , $a=5$ and $d=5$ in the sum formula, we have,

$Sum=\frac{19}{2}[2(5)+(19-1) 5]$

        $=\frac{19}{2}[10+(18) 5]$

        $=\frac{19}{2}[10+90]$

        $=\frac{19}{2}[100]$

$Sum=950$

Thus, the sum of all positive integral multiples of 5 less than 100 is 950

Learn more:

(1) What is the sum of the integers from 1 to 100 which are not divisible by 3 or 5

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(2) All the terms of an AP are natural numbers. the sum of its first nine terms lies between 200 and 220. if second term is 12 then find the common difference

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