Answer
$a_{100} = 200$
Work Step by Step
RECALL:
(1) The $n^{th}$ term of an arithmetic sequence can be found using the formula:
$a_n = a_1 + (n-1)d$
where $a_1$ = first term and $d$ = common difference
(2) The common difference $d$ can be found by subtracting any term from the next term of the sequence:
The given sequence has:
$a_1=2$;
$d=4-2=2$
Substitute these values into the formula for the $n^{th}$ term, we obtain:
$a_n=a_1 + (n-1)d
\\a_n=2+(n-1)2$
To find the 100th term, substitute $100$ for $n$ to obtain:
$a_{100} = 2+(100-1)(2)
\\a_{100}=2+99(2)
\\a_{100}=2+198
\\a_{100} = 200$
