Chapter 9 - Sequences and Series - 9-1 Mathematical Patterns - Lesson Check - Page 568: 4

$a_{n}=3n+2$

The sequence starts with $a_{1}=5=3+2$ So then $a_{2}=5+3=3+3+2=3*2+2$ $a_{3}=8+3=3+3+3+2=3*3+2$ $a_{4}=11+3=3+3+3+3+2=3*4+2$ etc... Note that the first part number being multiplied to $3$ is the same as the term number. Thus, if $n$ is the term number, then the explicit formula is $a_{n}=3n+2$