To identify the correct explicit formula for the sequence \(7, 10, 13, 16, 19, \ldots\), let's analyze the pattern in the sequence.
The first term is 7, and the sequence increases by 3 each time:
- \(10 - 7 = 3\)
- \(13 - 10 = 3\)
- \(16 - 13 = 3\)
- \(19 - 16 = 3\)
This indicates that the sequence is an arithmetic sequence with a first term \(a = 7\) and a common difference \(d = 3\).
The general formula for an arithmetic sequence can be expressed as: \[ f(n) = a + (n-1)d \] Plugging in the values: \[ f(n) = 7 + (n-1) \cdot 3 \]
Thus, the correct explicit formula for the sequence is: \[ f(n) = 7 + (n-1)3 \]
So the correct response is:
f(n)=7+(n−1)3