To find the function notation for the recursively defined sequence given by \( a_1 = -3 \) and \( a_n = a_{n-1} + 4 \), we can first compute the first few terms to identify the pattern.
- \( a_1 = -3 \)
- \( a_2 = a_1 + 4 = -3 + 4 = 1 \)
- \( a_3 = a_2 + 4 = 1 + 4 = 5 \)
- \( a_4 = a_3 + 4 = 5 + 4 = 9 \)
- \( a_5 = a_4 + 4 = 9 + 4 = 13 \)
The sequence appears to be an arithmetic sequence with a first term of \(-3\) and a common difference of \(4\).
The general form of an arithmetic sequence can be expressed as:
\[ a_n = a_1 + (n - 1)d \]
where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.
Substituting our values where \( a_1 = -3 \) and \( d = 4 \):
\[ a_n = -3 + (n - 1) \cdot 4 \]
Simplifying that equation:
\[ a_n = -3 + 4n - 4 = 4n - 7 \]
Thus, the function notation for the given sequence would be:
\[ a_n = 4n - 7 \]
Now, please provide the multiple-choice options so that we can identify which one matches our derived function notation.