Answer
$-1, 4, -9, 16, -25$
Work Step by Step
Let's evaluate $a_1, a_2, a_3, a_4, $and $a_5$ by plugging in $1, 2, 3, 4, $ and $5$ for each $n$.
We use PEMDAS (parentheses, exponentation, multiplication, division, addition, subtraction) to decide which operations go first.
\begin{align}
a_1 &= (-1)^11^2 = -1\cdot1^2 = -1\cdot 1 = -1 \\ \\
a_2 &= (-1)^22^2 = 1\cdot2^2 = 1 \cdot 4 = 4 \\ \\
a_3 &= (-1)^33^2 = -1\cdot3^2 = -1\cdot 9 = -9 \\ \\
a_4 &= (-1)^44^2 = 1\cdot4^2 = 1 \cdot 16 = 16 \\ \\
a_5 &= (-1)^55^2 = -1\cdot5^2 = -1\cdot25 = -25 \\ \\
\end{align}
