Final answer:
The nth term rule for the arithmetic sequence starting with 2, 9, 16, …, n, 23 is 'an = 7n - 5', with a common difference of 7 between terms.
Step-by-step explanation:
To determine the nth term rule for the given arithmetic sequence, we begin by identifying the common difference. The sequence presented is 2, 9, 16,..., …, n, 23. We can see that the difference between consecutive terms (9-2, 16-9, etc.) is 7. Thus, we can state that the common difference (d) in this sequence is 7.
Knowing that, the nth term of an arithmetic sequence can be found using the formula a_n = a_1 + (n-1)×d, where a_n is the nth term, a_1 is the first term, and d is the common difference.
The first term a_1 is 2. Substituting the values into the formula, the nth term becomes a_n = 2 + (n-1)×7, which simplifies to a_n = 7n - 5.
This is the nth term rule for the arithmetic sequence: the nth term equals 7 times n minus 5.