Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 834: 34

$d=4$. $a_1= 18$, $a_n= a_{n-1}+4$. $a_n= 4n+14$

1. Based on the given conditions, we have $a_{5}=a_1+4d=-2$ and $a_{13}=a_1+12d=30$, thus $8d=32$ and $d=4$. 2. We can find the first term $a_1=-2-4(4)=18$, and a recursive formula $a_n=a_{n-1}+d=a_{n-1}+4$. 3. We can find a formula for the nth term $a_n=a_1+(n-1)d=18+(n-1)(4)=4n+14$