Final answer:
The nth term rule for the quadratic sequence is n²/2 + n/2 + 8. After solving the system of equations to find a, b, and c using the first three terms of the sequence, we discovered the coefficients and applied them to find the 10th term, which is 63.
Step-by-step explanation:
To find the nth term rule for a quadratic sequence, we first need to determine the second difference. Since the given sequence is 9, 12, 17, 24, 33, we see that the first differences are 3, 5, 7, 9, which implies that the second differences are constant at 2. This tells us that the sequence is quadratic, and its nth term can be expressed as an² + bn + c.
To find a, b, and c, we will substitute terms of the sequence with their respective n values and solve the resulting system of equations. For the first term (n=1, term=9), second term (n=2, term=12), and third term (n=3, term=17), the equations are:
a + b + c = 9
4a + 2b + c = 12
9a + 3b + c = 17
Solving this system, we find that a = 1/2, b = 1/2, and c = 8. Thus, the nth term rule is n²/2 + n/2 + 8. To work out the 10th term in the sequence, we substitute n = 10 into our nth term rule to get:
10²/2 + 10/2 + 8 = 50 + 5 + 8 = 63
Therefore, the 10th term of the sequence is 63.