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To find the equation for the given sequence \(3, 12, 48, \ldots\), we need to determine the pattern that describes how each term relates to the previous term.

### Step 1: Identify the pattern
Looking at the sequence:
- The first term (\(n = 1\)) is 3.
- The second term (\(n = 2\)) is 12.
- The third term (\(n = 3\)) is 48.

We can see that each term is multiplied by 4 to get the next term:
- \(12 = 3 \times 4\)
- \(48 = 12 \times 4\)

Thus, the sequence has a common ratio of 4, making it a geometric sequence.

### Step 2: Write the formula for the general term
For a geometric sequence, the general term is given by:

\[
f(n) = a \cdot r^{(n-1)}
\]

where:
- \(a\) is the first term,
- \(r\) is the common ratio.

### Step 3: Substitute the values
- The first term \(a = 3\).
- The common ratio \(r = 4\).

So, the equation for the sequence is:

\[
f(n) = 3 \cdot 4^{(n-1)}
\]

Therefore, the boxes should be filled as follows:
- The first box: \(3\)
- The second box: \(4\)

Let me know if you would like further details or have any questions!

Here are some related questions you might find useful:
1. How do you find the nth term of an arithmetic sequence?
2. What is the sum of the first n terms of a geometric sequence?
3. How can you determine whether a sequence is arithmetic or geometric?
4. What are the differences between geometric and arithmetic sequences?
5. How do you calculate the common ratio in a geometric sequence?

**Tip:** When working with sequences, always identify whether the pattern involves addition (arithmetic) or multiplication (geometric) to determine the type of sequence.

Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. The sequence is 3, 12, 48, ...

Learn how to write an equation to describe the geometric sequence 3, 12, 48. This tutorial covers the general formula for geometric sequences and demonstrates how to calculate the common ratio and write the sequence equation. Suitable for Grades 6-9 students.

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