Question

3, 12, 48, 192, ...

Explanation:

Step1: Identify the common ratio

$\frac{12}{3}=4$, $\frac{48}{12}=4$, $\frac{192}{48}=4$

Step2: Define the nth term formula

For a geometric sequence, $a_n = a_1 \times r^{n-1}$, where $a_1=3$, $r=4$

Step3: Find the next term (5th term)

$a_5 = 3 \times 4^{5-1} = 3 \times 256$

Answer:

The sequence is a geometric sequence with a common ratio of 4. The next term is 768, and the nth term is given by $a_n = 3 \times 4^{n-1}$.