Answer
$5,18,9,30,15,48,24,12,6,3$
Work Step by Step
Calculate the first ten terms:
$$\begin{align*}
a_1&=5\\
a_2&=3(5)+3=18\\
a_3&=\dfrac{18}{2}=9\\
a_4&=3(9)+3=30\\
a_5&=\dfrac{30}{2}=15\\
a_6&=3(15)+3=48\\
a_7&=\dfrac{48}{2}=24\\
a_8&=\dfrac{24}{2}=12\\
a_9&=\dfrac{12}{2}=6\\
a_{10}&=\dfrac{6}{2}=3.
\end{align*}$$
We notice that $a_{11}=3(3)+3=12$ and the sequence $12,6,3$ repeats indefinitely.
