enter the correct answer in the box. the explicit formula for a certain geometric sequence is…

enter the correct answer in the box. the explicit formula for a certain geometric sequence is (f(n)=525(20)^{n - 1}). what is the exponential function for the sequence? write your answer in the form shown. (f(n)=\frac{a}{r}(r)^{n})

enter the correct answer in the box. the explicit formula for a certain geometric sequence is (f(n)=525(20)^{n - 1}). what is the exponential function for the sequence? write your answer in the form shown. (f(n)=\frac{a}{r}(r)^{n})

Answer

Explanation:

Step1: Identify values from given formula

The explicit formula for a geometric sequence is $f(n)=a\cdot r^{n - 1}$, and we have $f(n)=525(20)^{n - 1}$, so $a = 525$ and $r=20$.

Step2: Rewrite in $f(n)=\frac{a}{r}(r)^{n}$ form

Substitute $a = 525$ and $r = 20$ into $f(n)=\frac{a}{r}(r)^{n}$. Calculate $\frac{a}{r}=\frac{525}{20}=\frac{105}{4}$.

Answer:

$f(n)=\frac{105}{4}(20)^{n}$