To find the number that belongs in the blank space of the recursive formula for the given arithmetic sequence defined by the explicit formula \( a_n = 3 + (n - 1)(8) \), we first identify the common difference of the arithmetic sequence.
In the explicit formula, the term \( 8 \) represents the common difference of the sequence. This is because the formula can be rewritten as:
\[ a_n = 3 + 8(n - 1) \]
From this, we can see that each term increases by \( 8 \) as \( n \) increases by \( 1 \).
Therefore, the recursive formula for the sequence will be:
\[ a_n = a_{n-1} + d \]
where \( d \) is the common difference. Here, \( d = 8 \).
Thus, the recursive formula is:
\[ a_n = a_{n-1} + 8 \]
The number that belongs in the blank space in the recursive formula \( a_n = a_{n-1} + ___ \) is \( 8 \).
So the answer is:
D. 8