Chapter 12 - Section 12.2 - Arithmetic Sequences - 12.2 Exercises - Page 857: 37

$d=5$ $a_{n}=5n-1\ $ $ a_{5}=5\times 5-1=24\ $ $a_{100}=5\times 100-1=499$

$d=a_{n+1}-a_{n}=9-4=14-9=19-14=5$ $a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=4$ $a_{n}=a+\left( n-1\right) d=4+\left( n-1\right) \times 5=4+5n-5=5n-1$ $a_{n}=5n-1\Rightarrow a_{5}=5\times 5-1=24\ a_{100}=5\times 100-1=499$