Is it possible to find the iterative formula using its outputs?

[Spectre]

I was searching online to find a way to calculate an iterative formula by only using the outputs themselves, but unfortunately couldn't find anything.
For example, I can find when given the outputs 2, 4, 6 and 8.... and was wondering if there was a way to calculate the formula when given more complex numbers such as 1.09303249607, 1.09241529944, 0.95918481272 and 1.00107166501.

Any help is appreciated.

 

[Dr.Peterson]

I was searching online to find a way to calculate an iterative formula by only using the outputs themselves, but unfortunately couldn't find anything.
For example, I can findView attachment 30568 when given the outputs 2, 4, 6 and 8.... and was wondering if there was a way to calculate the formula when given more complex numbers such as 1.09303249607, 1.09241529944, 0.95918481272 and 1.00107166501.

Any help is appreciated.

In general, you can't find a formula for an unknown function from only a finite number of values, so I wouldn't expect this to be possible either.

But how is [imath]X_0=x+2[/imath] an iterative formula in the first place? Do you mean perhaps [imath]x_{n+1}=x_n+2[/imath]? And are you sure that is the only iterative formula that yields the sequence [imath]2, 4, 6, 8[/imath]?

 

[Spectre]

In general, you can't find a formula for an unknown function from only a finite number of values, so I wouldn't expect this to be possible either.

But how is [imath]X_0=x+2[/imath] an iterative formula in the first place? Do you mean perhaps [imath]x_{n+1}=x_n+2[/imath]? And are you sure that is the only iterative formula that yields the sequence [imath]2, 4, 6, 8[/imath]?

Sorry my bad, yes that is what I meant. And no, I didn't think that was the only one.

 

[Dr.Peterson]

And no, I didn't think that was the only one.

Then what does it mean to ask "Is it possible to find the iterative formula using its outputs?"

In any case, the answer is that even if you find some formula that gives your four numbers, it won't be particularly meaningful, particularly if you expect it to predict subsequent terms in a sequence obtained from somewhere else. There is no reason to think that it will be equivalent to whatever produced those numbers. A formula that gives your first three numbers probably won't give the fourth.