## College Algebra (11th Edition)

The first five terms are: $-2, 4, -6, 8, \text{ and } -10$
$\bf{\text{Solution Outline:}}$ 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 $-2, 4, -6, 8, \text{ and } -10 .$