# What is the sum of integers from 1 to 100 divisible by 2 or 5?

What is the sum of integers from 1 to 100 divisible by 2 or 5?

ReportAnswer 1

The sum is $3050$.

#### Explanation:

Ths sum of arithmetric progression is
$S = \frac{n}{2} \left(a + l\right)$, where $n$ is the number of terms, $a$ is the first term and $l$ is the last term.

The sum of integres $1$ to $100$ which is divisible by $2$ is
S_2=2+4+6+…100 = 50/2*(2+100)=2550
and, the sum of integers divisible by $5$ is
S_5=5+10+15+…100 =20/2*(5+100)=1050

You may think the answer is ${S}_{2} + {S}_{5} = 2550 + 1050 = 3600$ but this is wrong.

2+4+6+…100 and 5+10+15+…100 have common terms.
They are integers divisible by $10$, and their sum is
S_10=10+20+30+…100=10/2*(10+100)=550#

Therefore, the answer for this question is ${S}_{2} + {S}_{5} - {S}_{10} = 2550 + 1050 - 550 = 3050$.

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