Answer
$a_n=\left(\dfrac{2}{3}\right)^n$
Work Step by Step
The pattern shows that:
(1) The numerators involve powers of $2$.
first term's numerator = $2^1=2$
second term's numerator = $2^2=4$
third term's numerator = $2^3=8$
fourth term's numerator = $2^4=16$
(2) The denominators involve powers of $3$:
first term's denominator = $3^1 = 3$
second term's denominator = $3^2 =9$
third term's denominator = $3^3 = 27$
fourth term's denominator = $3^4=81$
Thus, the $n^{th}$ term of the sequence is:
$a_n=\dfrac{2^n}{3^n}=\left(\dfrac{2}{3}\right)^n$
