What is the next number in the sequence: 4,9,26,105,524?

1 Answer
Mar 6, 2017

Answer:

Without more information there is no unique answer.
However, one justifiable possibility is #color(green)(1789)#

Explanation:

We could assume that the series is definable in terms of a polynomial expression and take successive differences:

#{: (color(black)("number"),color(black)("1st order"),color(black)("2nd order"),color(black)("3rd order"),color(black)("4th order")), (,color(black)("difference"),color(black)("difference"),color(black)("difference"),color(black)("difference")), (4,,,,), (,5,,,), (9,,12,,), (,17,,50,), (26,,62,,228), (,79,,278,), (105,,340,,), (,419,,,), (524,,,,) :}#

If we assume that the series stabilizes with a #4^(th)# order difference of #228#,
we can generate the next line by back-filling from right to left:
#{: (color(black)("number"),color(black)("1st order"),color(black)("2nd order"),color(black)("3rd order"),color(black)("4th order")), (,color(black)("difference"),color(black)("difference"),color(black)("difference"),color(black)("difference")), (4,,,,), (,5,,,), (9,,12,,), (,17,,50,), (26,,62,,228), (,79,,278,), (105,,340,,color(red)(228)), (,419,,color(red)(506),), (524,,color(red)(846),,), (,color(red)(1265),,,), (color(red)(1789),,,,) :}#