Answer
a) $6; -3; 1.5; -0.75; 0.375;$
b) $r=-0.5$
c) See graph
Work Step by Step
We are given the sequence:
$$a_n=6(-0.5)^{n-1}.$$
a) Determine the first $5$ terms:
$$\begin{align*}
a_1&=6(-0.5)^0=6\\
a_2&=6(-0.5)^1=-3\\
a_3&=6(-0.5)^2=1.5\\
a_4&=6(-0.5)^3=-0.75\\
a_5&=6(-0.5)^4=0.375.
\end{align*}$$
b) The common ratio is the quotient between each number in the series and the number before it:
$$r=\dfrac{a_{n+1}}{a_n}=\dfrac{6(-0.5)^n}{6(-0.5)^{n-1}}=-0.5.$$
c) Graph the terms $a_1,a_2,a_3,a_4,a_5$:
