Answer
a) $2,\dfrac{1}{2},2,\dfrac{1}{2},2,\dfrac{1}{2},2,\dfrac{1}{2},2,\dfrac{1}{2}$
b) See graph
Work Step by Step
a) We calculate the first ten terms of the sequence $a_n=\dfrac{1}{a_{n-1}}$:
$$\begin{align*}
a_1&=2\\
a_2&=\dfrac{1}{a_1}=\dfrac{1}{2}\\
a_3&=\dfrac{1}{a_2}=\dfrac{1}{\dfrac{1}{2}}=2\\
a_4&=\dfrac{1}{a_3}=\dfrac{1}{2}\\
a_5&=\dfrac{1}{a_4}=\dfrac{1}{\dfrac{1}{2}}=2\\
a_6&=\dfrac{1}{a_5}=\dfrac{1}{2}\\
a_7&=\dfrac{1}{a_6}=\dfrac{1}{\dfrac{1}{2}}=2\\
a_8&=\dfrac{1}{a_7}=\dfrac{1}{2}\\
a_9&=\dfrac{1}{a_8}=\dfrac{1}{\dfrac{1}{2}}=2\\
a_{10}&=\dfrac{1}{a_9}=\dfrac{1}{2}.
\end{align*}$$
b) Graph the first ten terms:
