The given sequence is presented in the form $a_n = 4(2)^{n-1}$. This is already written as an exponential function of a geometric sequence.

Explanation:

• The general form of an exponential function for a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, where:
  • $a_1$ is the first term,
  • $r$ is the common ratio, and
  • $n$ is the term number.

In this case:

• $a_1 = 4$,
• $r = 2$,
• The exponent $(n-1)$ reflects the positioning of terms in the sequence.

Thus, this sequence follows the exponential function: $a_n = 4(2)^{n-1}$ which describes how each term is obtained by multiplying the previous term by 2.

Would you like to work on a specific part of this sequence or another similar question?

Here are some related questions you might find useful:

1. How do you identify the first term and common ratio in a geometric sequence?
2. How do you write an exponential function from a given geometric sequence?
3. How can you determine the 10th term of the sequence $a_n = 4(2)^{n-1}$?
4. How does the value of $n$ affect the terms of the sequence in exponential functions?
5. How would the sequence change if the base of the exponent was different (for example, $a_n = 4(3)^{n-1}$)?

Tip: To quickly find any term in a geometric sequence, you just need to plug in the value of $n$ into the exponential formula!