Common Ratio in Integer Geometric Sequence is Rational

Theorem

Let $\sequence {a_k}$ be a geometric sequence whose terms are all integers.

Then the common ratio of $\sequence {a_k}$ 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 Sequence is Rational.

$\blacksquare$