Answer
The explicit formula is $a_{n}$=48 $\times$ ($\frac{3}{4}$$)^{n-1}$
The recursive formula is $a_{1}$=48 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{3}{4}$.
Work Step by Step
The starting value is 48 so it is the $a_{1}$.
You have the sequence 48,36 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{36}{48}$=$\frac{3}{4}$.So the common ratio is $\frac{3}{4}$.Substitute the value of a1 and R into the explicit and recursive formula:
The explicit formula is $a_{n}$=$a_{1}$ $\times$ (r$)^{n-1}$ so the explicit formula is $a_{n}$=48 $\times$ ($\frac{3}{4}$$)^{n-1}$.
Use the recursive formula $a_{1}$=a, $a_{n}$=$a_{n-1}$$\times$r so the recursive formula is $a_{1}$=48 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{3}{4}$.
