Question 1188532: 1/2,-4/5,27/8,-256/11 ......
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
There is no way to find "THE" correct answer to any problem like this; ANY subsequent number(s) will form a valid sequence.
All you can do is try to find a logical pattern in the sequence that produces the given sequence and then use that pattern to GUESS what the next number(s) are.
In this example, one thing you have is the alternating signs; you need to incorporate that into your answer.
Then, ignoring the alternating signs, look at the numerators and denominators of the terms of the sequence separately and look for patterns:
numerators: 1, 4, 27, 256, ...
denominators: 2, 5, 8, 11, ...
A PROBABLE pattern for the denominators should be clear.
For the numerators, a PROBABLE pattern is harder to see; perhaps a special feature about the number 27 will give you the clue you need.
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