# Arithmetic progressions

**Number Theory**Level 5

How many arithmetic progressions of length 9 are there, such that the terms are integers from 1 to 70?

**Details and assumptions**

An **Arithmetic Progression** is a sequence of terms such that the difference between the consecutive terms is a constant. \( (1, 2, 3, 4), (1, 1, 1, 1), (4, 3, 2, 1)\) are all valid arithmetic progressions of length 4.