Answer
$\left\{\begin{array}{l}
a_{1}=81,\\
a_{n}=a_{n-1}/3
\end{array}\right.$
Work Step by Step
We note that all the given terms are powers of 3:
$81\div 3=27\qquad\rightarrow\qquad a_{2}=a_{1}/3$
$27\div 3=9\qquad\rightarrow\qquad a_{3}=a_{2}/3$
$9\div 3=3\qquad\rightarrow\qquad a_{4}=a_{3}/3$
$3\div 3=1\qquad\rightarrow\qquad a_{5}=a_{4}/3$
$1\div 3=1/3\qquad\rightarrow\qquad a_{6}=a_{5}/3$
$...$
A general rule:$\qquad a_{n}=a_{n-1}/3$
A recursive rule for the sequence:
$\left\{\begin{array}{l}
a_{1}=81,\\
a_{n}=a_{n-1}/3
\end{array}\right.$
