SOLUTION: what is the next number in this series 4, 7, 16, 43, 124

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Question 829363: what is the next number in this series 4, 7, 16, 43, 124
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is surely an exponential growth. Pick your base, either e or 10, or whatever you like; and try to fit to y=a%2Ab%5E%28kx%29.
Use x as the index for your domain of Natural Numbers.

The exponential equation can be put into a linear form:
log%28%28y%29%29=log%28%28a%2Ab%5E%28kx%29%29%29
log%28%28y%29%29=log%28%28a%29%29%2Bkx%2Alog%28%28b%29%29---as a linear equation.
Recognize that log(b) for your chosen base of b will be 1.
log%28%28y%29%29=log%28%28a%29%29%2Bkx
highlight_green%28log%28%28y%29%29=kx%2Blog%28%28a%29%29%29
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Your function NOW is log(y) for the vertical component and x for the horizontal component. This is an equation for a line, which your actual data may likely fit well. The slope is k, and the vertical axis intercept is log(a).

Now knowing k and log((a)), your next value for x should be 6. Use this to determine log((y)), and then find y.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
what is the next number in this series 4, 7, 16, 43, 124


Rule: t%5Bn%5D+=+t%5Bn+-+1%5D+%2B+3%5E%28n+-+1%29, with t%5B1%5D+=+4

Thus, the 6th term is: t%5B6%5D+=+t%5B6+-+1%5D+%2B+3%5E%286+-+1%29, or t%5B6%5D+=+t%5B5%5D+%2B+3%5E%285%29.

Do a check after!! 



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