Question

What is the nth term of the quadratic sequence 3 11 24 45

Answer 1

9514 1404 393

Answer:

  $a_n=\dfrac{1}{2}n^3-\dfrac{1}{2}n^2+6n-3$

Step-by-step 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 ...

  $a_n=\dfrac{1}{2}n^3-\dfrac{1}{2}n^2+6n-3$