Answer
Recursive formula: $a_{1}=2$, $a_{n}=a_{n-1}+2$
Explicit formula:$a_{n}=2n$
Work Step by Step
The first term is $2$ and the common difference is $4-2=2$.
$\text{Explicit formula}$:
The explicit formula is $a_{n}=a_{1}+(n-1)d$ where $a_1$=first term and $d$=common difference. Substitute the values of the common difference and the first term to obtain:
$a_{n}=2+(n-1)2$
$a_{n}=2+(2n-2)$
$a_{n}=2n$
$\text{Recursive formula}$:
The recursive formula is $a_{n}=a_{n-1}+d$
Substitute the value of $d$ to obtain:
$a_{n}=a_{n-1}+2$ where $a_1=2$
