Question

What is the nth term of the quadratic sequence

3 11 24 45

Answer 1

9514 1404 393

Answer:

`a_n=(1)/(2)n^3-(1)/(2)n^2+6n-3`

Explanation:

The first differences are 8, 13, 21. The second differences are 5, 8. The second differences are not constant, so this is not a quadratic sequence.

If we assume it is a cubic sequence, a calculator tells us the formula is ...

`a_n=(1)/(2)n^3-(1)/(2)n^2+6n-3`