Question

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

Answer 1

The sum is `3050`.

Explanation:

Ths sum of arithmetric progression is
`S=n/2(a+l)`, 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`.