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.