To find the nth term of the sequence 7, 12, 17, 22, ..., we first need to determine the pattern in the sequence.
The sequence has the following characteristics:
- The first term (n = 1) is 7.
- The second term (n = 2) is 12.
- The third term (n = 3) is 17.
- The fourth term (n = 4) is 22.
To find the common difference, we can subtract successive terms:
12 - 7 = 5
17 - 12 = 5
22 - 17 = 5
The common difference is 5, indicating that this is an arithmetic sequence.
The nth term of an arithmetic sequence can be found using the formula: \[ a_n = a_1 + (n - 1) \cdot d \] where \(a_n\) is the nth term, \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
For this sequence:
- \(a_1 = 7\)
- \(d = 5\)
Now, substituting these values into the formula: \[ a_n = 7 + (n - 1) \cdot 5 \] \[ a_n = 7 + 5n - 5 \] \[ a_n = 5n + 2 \]
Thus, the expression to find the nth term of the sequence is: \[ a_n = 5n + 2 \]
The correct answer is D. 5n + 2.