Question 1130148: Can you help me find the next number in this sequence; 1869,5283, 0897,2047, 1901? Or its equation to which this series was created? Thank you.
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
The 3rd term being "0897" instead of "897" suggests that the sequence is not created by an equation or formula. It might be, for example, the 75th through 94th digits after the decimal in pi, in 5 groups of 4 digits each.
I can show you a way to find a POSSIBLE next number for any sequence like this. If the sequence is in fact created by an equation or formula, then the answer you get by this method might have a reasonably good chance of giving you the "right" answer.
However, it should be noted that NO problem like this can be solved for a single "right" answer mathematically; ANY next number will make a valid sequence.
Here is a way to find a formula that will generate any given sequence of numbers.
(1) Any sequence of n numbers can be created by a polynomial of degree (n-1) (or less). The given sequence has 5 terms, so it can be created by a polynomial of degree 4.
(2) Call the 4th degree polynomial that creates the sequence
(3) Solve a system of 5 equations in a, b, c, d, and e using the given 5 terms:
Trying to solve a system of equations with numbers like that is absurd. A graphing calculator that performs matrix operations does a good quick job.
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