What is the nth term of the quadratic sequence 5 20 45 80 125?

Answer 1

{5, 20, 45, 80, 125} = 5{1, 4, 9, 16, 25} = 5{1², 2², 3², 4², 5²}

→ U{n} = 5n²

Answer 2

To find the nth term of a quadratic sequence, we need to identify the pattern and then create a formula. In this case, the sequence appears to be increasing by the squares of consecutive odd numbers (1^2, 3^2, 5^2, 7^2, 9^2). The formula for the nth term of this quadratic sequence is n^2 + 4n + 1.

Answer 3

Oh, dude, calm down with the math! So, the nth term of a quadratic sequence can be found using the formula an = n^2 + 4n + 1. Just plug in the value of n, which in this case is 1, 2, 3, 4, 5 for the terms 5, 20, 45, 80, 125 respectively. Like, it's just a fancy way of saying "plug and chug."

Answer 4

Well, darling, the nth term of a quadratic sequence can be found by taking the difference between consecutive terms and then finding a pattern. In this case, the differences are 15, 25, 35, so it's clear the pattern is increasing by 10 each time. Therefore, the nth term is n^2 * 5. You're welcome, sweetie.