Final answer:
To find the nth term of the sequence 9, 16, 23, 30, 37, we use the formula for the nth term of an arithmetic sequence. The sequence has a common difference of 7, leading to the nth term formula 7n + 2.
Step-by-step explanation:
To determine the nth term of the given sequence 9, 16, 23, 30, 37, we first find the common difference by subtracting any term from the term that follows it. For instance, 16 - 9 = 7 and 23 - 16 = 7, so the common difference is 7. This indicates that the sequence is an arithmetic sequence.
Next, we use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
For this sequence, a1 = 9 and d = 7, so we have an = 9 + (n-1)(7) = 9 + 7n - 7 = 7n + 2. Therefore, the nth term of the sequence is 7n + 2.