Find next term of the series ${-3, 2, -4/3, 8/9, -16/27}$ The problem is to find out the next term of the series {$-3$, $2$, $-4/3$, $8/9$, $-16/27$}. 
I have tried various things but haven't been able to come up with an answer. Is there a method to solve questions like these? Or is it just intuition? Please help.
The question actually required me to find the general term.
 A: The next term problem is generally not a math problem, there is an infinity of possibilities, unless you spot a pattern. Possibly, starting from $k=0$, you have:
$$s_k = -(-2)^k.3^{1-k}\,,$$
or 
$$s_k = -3 \left(\frac{-2}{3}\right)^k\,.$$
Works for the five first terms.
In your case, it is easy to spot powers of $2$ and powers of $3$, and the alternating sign. Powers suggest computing ratios of terms. The alternating sign suggests it is not too complicated, because $-1,1,-1,-1,\ldots$ is not.
Simple techniques are computing differences or ratios, or differences of differences, etc. And recognizing standard series.  But this falls short fast with $5$ terms. 
But you never know what the person who asks you the question has in mind. What would one do with $8,12,15,20,23,28,32,35,38,43,45,50,56$?
This is the cumulated number of letters from words of the lyrics of Shine on you crazy diamond, by the Pink Floyd, which I am currently listening to. So the next is $59$, because "now" follows "Remember  when you were young, you shone like the sun. Shine on you crazy diamond".
