Answer:an = 3 * 4^(n-1)
Explanation:
The sequence 3, 12, 48 can be understood as a geometric sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio.
To find the common ratio in this sequence, we divide each term by its previous term:
12 / 3 = 4
48 / 12 = 4
The common ratio is 4, meaning that each term in the sequence is obtained by multiplying the previous term by 4.
Starting with the first term 3, we can find the next terms by multiplying each term by 4:
3 * 4 = 12
12 * 4 = 48
48 * 4 = 192
So, the sequence continues as 3, 12, 48, 192, and so on, with each term being obtained by multiplying the previous term by 4.
In general, the nth term of a geometric sequence can be found using the formula:
an = a1 * r^(n-1)
where a represents the nth term, a1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
Therefore, in this sequence, the nth term can be calculated as:
an = 3 * 4^(n-1)
Please note that without further context or information, it is difficult to determine if this is the only possible sequence or if there are alternative patterns that could also fit the given terms.