# How do you write the expression for the nth term of the sequence given 0, 3, 8, 15, 24,...?

Aug 31, 2017

${n}^{2} - 1$

#### Explanation:

If you try to find the differences between the numbers of the sequence, you'll notice that they go up by 3, 5, 7 and 9. These differences have a second difference of 2(i.e. they go up by 2).

Remember that the structure of a quadratic sequence, is an^2±bn±c

So, you halve the second difference in order to get the $a$ coefficient, which is 1, to get:
n^2±bn±c

Now, if you subtract the original sequence by the sequence of ${n}^{2}$, you'll notice that there is a common difference, -1. Therefore, there is no additional sequence that you have to take into consideration.

Thus, the answer is: ${n}^{2} - 1$!

(Also, if you know your squared numbers well, you will notice that it is ${n}^{2} - 1$ without having to do much calculation :D)

Hope this helps!