Final answer:
The nth term of the quadratic sequence 3, 8, 15, 24 is given by the formula n^2 + 2n, where n is the position of the term in the sequence starting with n=1.
Step-by-step explanation:
The student has asked to find the nth term of a quadratic sequence. The given sequence is 3, 8, 15, 24. To determine the pattern, we observe that the differences between each term are increasing by a constant amount, which is characteristic of a quadratic sequence. The differences are 5, 7, 9, and so forth, each increased by 2. To find a formula for the nth term, we recognize that this sequence can be written as n2 + 2n, where n starts at 1. This is because:
- When n=1, 12 + 2(1) = 3, which is the first term.
- When n=2, 22 + 2(2) = 8, which is the second term.
- When n=3, 32 + 2(3) = 15, which is the third term.
- When n=4, 42 + 2(4) = 24, which is the fourth term.
Therefore, the nth term for this sequence is n2 + 2n.