# Clever 4-term Sequences

**Number Theory**Level 5

How many 4-term geometric sequences have all four terms positive integers less than or equal to 100?

**Details and assumptions**

Clarification: The sequence \(1, 2, 4, 8\) is different from the sequence \( 8, 4, 2, 1\). The sequence \(1, 1, 1, 1\) is the same as the 'flipped sequence' \( 1, 1, 1, 1\).