Answer
a) $\dfrac{5}{2};-\dfrac{5}{4};\dfrac{5}{8};-\dfrac{5}{16};\dfrac{5}{32};$
b) $r=-\dfrac{1}{2}$
c) See graph
Work Step by Step
We are given the sequence:
$$a_n=\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^{n-1}.$$
a) Determine the first $5$ terms:
$$\begin{align*}
a_1&=\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^0=\dfrac{5}{2}\\
a_2&=\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^1=-\dfrac{5}{4}\\
a_3&=\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^2=\dfrac{5}{8}\\
a_4&=\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^3=-\dfrac{5}{16}\\
a_5&=\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^4=\dfrac{5}{32}.
\end{align*}$$
b) The common ratio is the quotient between each number in the series and the number before it:
$$r=\dfrac{a_{n+1}}{a_n}=\dfrac{\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^n}{\dfrac{5}{2}\left(-\dfrac{1}{2}\right)^{n-1}}=-\dfrac{1}{2}.$$
c) Graph the terms $a_1,a_2,a_3,a_4,a_5$:
