Determine if the next number will be larger or smaller

[msticky]

4
5
7
1
1
2
8
3
35
2

If I get the average of the numbers above I get 6.8

Its seems to me that I should be able to determine if the next number will be larger or smaller
by the last few numbers.

For instance the second last value of 35 is large, should I not get a series of smaller numbers?

Can I determine if the next numbers will be lower and when they may get larger?

 

[Mandelbroth]

4
5
7
1
1
2
8
3
35
2

If I get the average of the numbers above I get 6.8

Its seems to me that I should be able to determine if the next number will be larger or smaller
by the last few numbers.

For instance the second last value of 35 is large, should I not get a series of smaller numbers?

Can I determine if the next numbers will be lower and when they may get larger?

There is no way to determine a unique next number unless you give a rule for how they are generated.

For example, I can just say that the next number is $3+5i$. This is perfectly true if I define a pointwise sequence with the last term being $3+5i$.

 

[Boorglar]

Without information on the rule, probability distribution and/or the allowed range of numbers, there's no way to tell.