Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 30

$\{a_n\}=\dfrac{2^n}{3^{n}}=(\dfrac{2}{3})^n$

We notice from the sequence that the numerator starts from $1$ and gets multiplied by $2$ with each new term. The denominator starts from $3$ and gets multiplied by $3$ with each new term. So, we determine the sequence pattern as: $\{a_n\}=\dfrac{1*2^n}{1*3^{n}}=(\dfrac{2}{3})^n$ .