The given sequence is: \( a_6 = 3, 12, 48 \), and we need to find the nth term of the sequence.

Let’s observe how the terms progress:

- First term: \( 3 \)
- Second term: \( 12 \)
- Third term: \( 48 \)

To find a pattern, let's check if the ratio between consecutive terms is constant:

- \( \frac{12}{3} = 4 \)
- \( \frac{48}{12} = 4 \)

Since the ratio is constant, this indicates that the sequence is geometric, where the first term \( a_1 = 3 \) and the common ratio \( r = 4 \).

The formula for the nth term of a geometric sequence is given by:

\[
a_n = a_1 \times r^{n-1}
\]

Substitute the known values:

\[
a_n = 3 \times 4^{n-1}
\]

So, the nth term of the sequence is:

\[
\boxed{a_n = 3 \times 4^{n-1}}
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. What is the 5th term of this sequence?
2. How do you find the sum of the first n terms of a geometric sequence?
3. Can you explain how to derive the formula for the nth term of a geometric sequence?
4. What happens if the common ratio of a sequence is less than 1?
5. How do you determine if a sequence is arithmetic or geometric?

**Tip:** For geometric sequences, the ratio between consecutive terms is always constant.

Find the nth term of the sequence a6=3, 12, 48.

Discover how to find the nth term of the geometric sequence 3, 12, 48 with a step-by-step explanation. This guide covers geometric progression, key formulas, and how to identify the common ratio. Suitable for students in Grades 8-10.

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