Which function below represents the arithmetic sequence 3, 7, 11, 15...?
The general form of an arithmetic sequence is given by the formula:
\[a_n = a_1 + (n - 1)d\]
where \(a_n\) is the \(n\)th term of the sequence, \(a_1\) is the first term, and \(d\) is the common difference between consecutive terms.
In this case, the sequence starts with 3, so \(a_1 = 3\).
The common difference between consecutive terms is 4 (since 7 - 3 = 4, 11 - 7 = 4, and so on).
Using the formula, the nth term of the arithmetic sequence can be written as:
\[a_n = 3 + (n - 1) \cdot 4\]
Simplifying this expression:
\[a_n = 3 + 4n - 4\]
\[a_n = 4n - 1\]
Therefore, the function that represents the arithmetic sequence 3, 7, 11, 15... is \(f(n) = 4n - 1\).