Question

Find the number of positive numbers less than 2020, which can be written as the sum of five consecutive positive numbers.

Answer 1

Integers*?

Let
`n` be the smallest of these five consecutive integers. Then the sum of the five consecutive integers is
`(5(2n+4))/(2)=5n+10,` so we seek the largest positive integer
`n` such that
`5n+10<2020.` Solving this inequality, we find that
`n<402,` so there are
`\boxed{401}` such positive integers.