Final answer:
The nth term formula for the arithmetic sequence 15, 24, 33 is a_n = 9n + 6. We used the arithmetic sequence formula a_n = a_1 + (n - 1)d, where a_1 is the first term (15) and d is the common difference (9).
Step-by-step explanation:
To determine the nth term of the sequence 15, 24, 33, we can observe that the sequence is arithmetic since the difference between each term is constant. In an arithmetic sequence, the nth term is given by the formula an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
Steps to Find the Nth Term:
Determine the first term (a1). In this sequence, a1 is 15.
Calculate the common difference (d) by subtracting the first term from the second term, which gives us 24 - 15 = 9. Apply the formula for the nth term: an = 15 + (n - 1)×9.
Simplify the formula to an = 15 + 9n - 9.
Further simplify to get an = 9n + 6, which is the formula for the nth term of the sequence.