Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 645: 9

$5, 3, 1, -1, -3$

$\bf{\text{Solution Outline:}}$ To find the first $5$ terms, keep adding the given common difference to the given first term. $\bf{\text{Solution Details:}}$ In the given sequence, $a_1= 5 ,$ and $d= -2 .$ Then the second term is \begin{array}{l}\require{cancel} a_2=a_1+d \\\\ a_2=5+(-2) \\\\ a_2=5-2 \\\\ a_2=3 ,\end{array} the third term is \begin{array}{l}\require{cancel} a_3=a_2+d \\\\ a_3=3+(-2) \\\\ a_3=3-2 \\\\ a_3=1 ,\end{array} the fourth term is \begin{array}{l}\require{cancel} a_4=a_3+d \\\\ a_4=1+(-2) \\\\ a_4=1-2 \\\\ a_4=-1 ,\end{array} and the fifth term is \begin{array}{l}\require{cancel} a_5=a_4+d \\\\ a_5=-1+(-2) \\\\ a_5=-1-2 \\\\ a_5=-3 ,\end{array} Hence, the first $5$ terms are $ 5, 3, 1, -1, -3 .$