Question

Convert each geometric sequence into an exponential function.3, 12, 48, 192,….

Answer 1

Use the next formula to write a geometric sequence as a exponential function:

$f(n)=f(1)\cdot r^{n-1}$

f(1) is the first term

r is the common ratio

1. Find the common ratio: Divide each term into the previous term

$\begin{gathered} \frac{12}{3}=4 \\ \\ \frac{48}{12}=4 \\ \\ \frac{192}{48}=4 \end{gathered}$

Common ratio: 4

2. Use the first term (3) and the common ratio (4) in the formula above:

$f(n)=3\cdot4^{n-1}$

Then, the given sequece written in form of a exponential function is:

$f(n)=3\cdot4^{n-1}$