This problem involves arithmetic sequences, which are sequences where the difference between consecutive terms is constant.
In this case, the arithmetic sequence is defined by a recursive formula:
A1 is the first term and it equals 6.
The nth term, An, is the (n - 1)th term, An-1, minus 3.
From the recursive formula, we can derive the explicit form of the sequence.
Firstly, the common difference, d, in an arithmetic sequence is found by subtracting any term in the sequence from the subsequent term. Here, the common difference is -3, since the nth term is obtained by subtracting 3 from the previous term.
The general form for an arithmetic sequence is An = A1 + (n - 1)d. A1 represents the first term in the sequence, d is the common difference, n refers to the term number, and An is the term you wish to find.
In this arithmetic sequence, A1 is 6 and the common difference, d, is -3.
If we plug these values into the general formula, we get:
An = 6 + (n - 1)(-3).
In this way, option A, An = 6 + (n - 1)(-3), is the explicit formula for this sequence.