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

How do you write the expression for the nth term of the sequence given 0,3,8,15,24,...?
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SlowlFeet45
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 $a{n}^{2}±bn±c$
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: ${n}^{2}-1$ !