RO-TST 1999 Problem 7

Prove that for any integer $n$ , $n\geq 3$ , there exist $n$ positive integers $a_1,a_2,\ldots,a_n$ in arithmetic progression, and $n$ positive integers in geometric progression $b_1,b_2,\ldots,b_n$ such that $$b_1 < a_1 < b_2 < a_2 <\cdots < b_n < a_n .$$ Give an example of two such progressions having at least five terms.

Mihai Baluna