What is the nth term for 3 11 21 33 47 63?

Answer 1

t(n) = n2 + 5n - 3

Answer 2

To find the pattern in the sequence 3, 11, 21, 33, 47, 63, we first need to calculate the differences between consecutive terms: 8, 10, 12, 14, 16. We notice that the differences are increasing by 2 each time. This indicates a quadratic relationship. By finding the second differences (which are constant at 2), we can conclude that the sequence follows a quadratic equation of the form an^2 + bn + c. Therefore, the nth term for this sequence is given by the quadratic equation an^2 + bn + c, where a = 1, b = 2, and c = 0.

Answer 3

dd