Answer
Just substitute $c_i$ by the index, starting from $0$, because the sequence is defined for $i\geq1$, substitute the values and calculate.
Work Step by Step
$i \geq 0$:
$\begin{split}
c_i & = \frac{(-1)^i}{3^i} = \frac{(-1)^i}{3^i} \\
& \\
c_0 & = \frac{(-1)^0}{3^0} = \frac{1}{1} = 1 \\
& \\
c_1 & = \frac{(-1)^1}{3^1} = \frac{-1}{3} \\
& \\
c_2 & = \frac{(-1)^2}{3^2} = \frac{1}{9} \\
& \\
c_3 & = \frac{(-1)^3}{3^3} = \frac{-1}{27}\\
& \\
\end{split}$
