Answer
The recursive formula is $a_{1}$=100 and $a_{n}$=$a_{n-1}$ $\times$ ($\frac{1}{2}$).
Work Step by Step
Use the recursive formula $a_{1}$=a, $a_{n}$=$a_{n-1}$$\times$r.
The starting value is 100 so it is the $a_{1}$
You have the sequence 100,50,25 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{50}{100}$=$\frac{1}{2}$ and r=$\frac{25}{50}$=$\frac{1}{2}$.So the common ratio is $\frac{1}{2}$.Substitute the value of a1 and R into the recursive formula:
The recursive formula is $a_{1}$=100 and $a_{n}$=$a_{n-1}$ $\times$ ($\frac{1}{2}$).
