Question 146
The terms $a_1, a_2, a_3, a_4, a_5$ of a geometric sequence are positive integers. All are less than $2008$, $a_2$ is divisible by $5$, $a_3$ is divisible by $4$, $a_4$ is divisible by $3$, $a_1$ is not divisible by $6$ and no prime number divides all five of them. Determine the terms of this sequence.