Answer
The first five terms are: $
-2,
4,
-6,
8, \text{ and }
-10
$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the first five terms of the given sequence, $
a_n=(-1)^n(2n)
,$ substitute $n$ with the numbers from $1$ to $5.$
$\bf{\text{Solution Details:}}$
Substituting $n$ with $1$, then the first term is
\begin{array}{l}\require{cancel}
a_1=(-1)^1(2\cdot1)
\\\\
a_1=(-1)(2)
\\\\
a_1=-2
.\end{array}
Substituting $n$ with $2$, then the second term is
\begin{array}{l}\require{cancel}
a_2=(-1)^2(2\cdot2)
\\\\
a_2=(1)(4)
\\\\
a_2=4
.\end{array}
Substituting $n$ with $3$, then the third term is
\begin{array}{l}\require{cancel}
a_3=(-1)^3(2\cdot3)
\\\\
a_3=(-1)(6)
\\\\
a_3=-6
.\end{array}
Substituting $n$ with $4$, then the fourth term is
\begin{array}{l}\require{cancel}
a_4=(-1)^4(2\cdot4)
\\\\
a_4=(1)(8)
\\\\
a_4=8
.\end{array}
Substituting $n$ with $5$, then the fifth term is
\begin{array}{l}\require{cancel}
a_5=(-1)^5(2\cdot5)
\\\\
a_5=(-1)(10)
\\\\
a_5=-10
.\end{array}
Hence, the first five terms are $
-2,
4,
-6,
8, \text{ and }
-10
.$
