Final answer:
The nth term of the sequence 5, 20, 45, 80, 125 is a quadratic expression. The sequence reflects consecutive differences of multiples of 5, which supports a quadratic nature. The nth term is defined by the formula Tn = n^2 + 4n.
Step-by-step explanation:
To find the nth term of the given sequence (5, 20, 45, 80, 125), we need to determine a pattern or rule that generates these terms. Observing the differences between consecutive terms, we get:
- 20 - 5 = 15
- 45 - 20 = 25
- 80 - 45 = 35
- 125 - 80 = 45
The differences are consecutive multiples of 5, indicating this is a sequence of quadratic nature. The nth term can be represented by a quadratic expression of the form an2 + bn + c. Using the data points and solving a system of equations, we can find that the nth term is defined by:
Tn = n2 + 4n