Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 834: 23

$a_{100} =200$

The $n^{th}$ term of an arithmetic sequence is given by the formula: $a_n = a_1 + (n-1)d (1)$ where $a_1 = \ First \ Term; \\ d = \ Common \ Difference$ We have: $a_1=2 \\ d=a_2-a_1=4-2=2$ We will substitute the above data into formula (1) to obtain: $a_n=2+(2) (n-1)$ In order to compute the $100th$ term, we need to plug in $100$ for $n$ into the above form to obtain: $a_{100} = 2+(2) (100-1) =2+(99)(2)$ So, $a_{100} =200$