What are the common techniques to solve this type of series? I found this series: $2;10;32;88$ My teacher has told me that there is no methodology or equation to find the n-term ( Im be in high school yet ). It really is that? If so, at least there are techniques? It takes a lot of time to do the test-error, thinking practically at random. Things like this: $-2;4;-6;8$ can be solved more easy, because is a it is a more concordant pattern. = $2n(-1)^n$ ( With $a_1$ as first index)

You like to fit these values $$(1,2);(2,10);(3,32);(4,88)$$ into a model.

While there are many different ways to find such a model, it is easy to find a polynomial to fit the data.

Check the following model:

$$a_n=(44/3)(n-1)(n-2)(n-3)-16(n-1)(n-2)(n-4)+5(n-1)(n-3)(n-4)-(1/3) (n-2)(n-3)(n-4)$$

The simplified polynomial takes the form $$ a_n=\frac {1}{3}(10n^3-39n^2+71n-36)$$ Your data fits perfectly in this model.

Note that the answer is not unique because there are many curves passing through your data.