When a sequence is NOT arithmetic OR geometric, how can you determine the formula for the nth term?
I do not understand how to get the formula when this situation occurs.
Can someone please help me? EXPLAIN WITH DETAIL please!!
This depends on the series you're given. There's no formula or standard way of getting the $\displaystyle n-th$term in general. In the case of an arithmetic or geometric series it just so happens that the deriving a formula is easy and obvious. Do you have a specific series in mind?
As David said it is very situational, it can be easy
$\displaystyle -1,\frac{1}{2},\frac{-1}{6},\frac{1}{24},\cdots$ can easily be identified to be $\displaystyle a_n=\frac{(-1)^n}{n!}$
But some are not so easy. It just comes from experience. And just as David said, if you have any specific problems you need help with just post them and I am sure someone will be kind enough to help.