Common Ratio in Integer Geometric Sequence is Rational

Theorem
Let $\left\langle{a_k}\right\rangle$ be a geometric progression whose terms are all integers.

Then the common ratio of $\left\langle{a_k}\right\rangle$ is rational.

Proof
From Integers form Subdomain of Rationals it follows that $a_k \in \Q$ for all $0 \le k \le n$.

The result follows from Common Ratio in Rational Geometric Progression is Rational.