The geometric sequence given in the image is:

$g_n = 3 \cdot \left( \frac{1}{4} \right)^{n-1}$

To rewrite this sequence in function form, we substitute $n$ with $x$, since we're expressing it as a function of $x$:

$f(x) = 3 \cdot \left( \frac{1}{4} \right)^{x-1}$

Thus, the function form of the sequence is:

$f(x) = 3 \cdot \left( \frac{1}{4} \right)^{x-1}$

Would you like more details on geometric sequences, or have any other questions?

Related questions:

1. What is the general formula for a geometric sequence?
2. How can you find the nth term of a geometric sequence?
3. What is the common ratio of a geometric sequence, and how do you identify it?
4. How do you find the sum of the first $n$ terms of a geometric series?
5. What happens to the terms of a geometric sequence as $n$ increases, particularly when the common ratio is between 0 and 1?

Tip:

When working with geometric sequences, remember that the common ratio determines whether the terms will grow or shrink as $n$ increases.