SOLUTION: 2 , 6, -18, -54, ... What will be the next term. What will be the formula?

Question 1119057: 2 , 6, -18, -54, ... What will be the next term. What will be the formula?

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Although there is an apparent pattern in this sequence, it is in fact impossible to answer this question (or any like it), because any subsequent numbers will form a valid sequence.

Assuming the apparent pattern continues, there are many ways you could define a formula that produces the sequence. With the signs of the terms changing on only every OTHER term, an explicit formula would be messy.

One example of a recursive formula that defines the sequence could be
.. t(1) = 2
.. t(n) = 3*t(n-1) if n is even
.. t(n) = -3*t(n-1) if n is odd and greater than 1
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.
From the Math point of view, the question "what is the next term in the sequence ?" MAKES NO SENSE, until the sequence/the pattern is not defined.

Those who solve (guess) puzzles, have another point of view, but guessing puzzles is not Math,
and in this site we do not solve puzzles and do not provide help to such people.

Next door (I mean, look for other site), please !

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