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Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.

One possible solution is to consider U(n) = (2*n^4 - 20*n^3 + 97*n^2 - 715*n + 2424)/6 for n = 1, 2, 3, ...and according to that solution, the next number is -17.

Q: What number is next 298 209 129 58 4?

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At each step the number being subtracted is reduced by 9 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57..........which is the next number.

-57

-57 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57 notice every number is subtracted by 9 less than the previous number's subtrator

-57

-57 (each number that is subtracted from the first is 9 different from the previous (i.e. 298-89=209-80=129-71=58-62=-4-53=-57). As you can see, the amounts that are substracted are 89, 80, 71, 62, 53 (all 9 different from the one before it.)

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-57

At each step the number being subtracted is reduced by 9 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57..........which is the next number.

-57

-57

-57

-57

-57 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57 notice every number is subtracted by 9 less than the previous number's subtrator

-57

The sequence is formed by subtracting 89 at the first step and then reducing this figure by 9 at each successive step. 298 - 89 = 209 209 - 80 = 129 129 - 71 = 58 58 - 62 = -4 -4 - 53 = -57........this is the next number in the series.

298 less 209 is 89 209 less 129 is 80 129 less 58 is 71 58 less -4 is 62 The result of each subsequent equation is 9 less than the previous one (89, 80, 71...). The next result is going to be 62-9=53. The first number in each equation above is the same as the second number in the previous equation: 298 less 209 is 89 209 less 129 is 80So, the next equation will be: -4 less X is 53 Therefore, X is the next number in the original sequence, which resolves to: -57

The difference between one number and the next in the sequence is decreasing by 9 each time. Therefore, the difference between -4 and the next number will be equal to 62 - 9 = 53. The next number is therefore equal to -4 - 53 = -57.

The answer that follows is -57 Logic is explained in the related link to another wiki question.