Answer
Recursive formula: $a_{1}=27$, $a_{n}=a_{n-1}-12$
Explicit formula: $a_{n}=-12n+39$
Work Step by Step
The first term is $27$ and the common difference is $15-27=-12$.
$\text{Explicit formula}$:
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:
$a_{n}=27+(n-1)(-12)$
$a_{n}=27+(-12n+12)$
$a_{n}=-12n+39$
$Recursive formula$:
The recursive formula is $a_{n}=a_{n-1}+d$.
Substitute the value of $d$ to obtain:
$a_{n}=a_{n-1}-12$ where $a_1=27$
