How to figure out the what the next number would be?

Question

Let's say I have a sequence of numbers simpilar to this: 1, 2, 5, 3, 34, 5, 7, 11, 22, 45, 56. How can I figure out what would be the next number? I guess I will firstly have to figure out some general idea about (or a general pattern or a principle of) the nature of the development hidden behind these numbers, and then, based on that principle, figure out the next possible number. But how?

Answer 1

The way I do it is to set up a table with rows and columns. Then, using the top row (or you could use the first column, as you wish), you write the numbers every second column.
In the second row, write the difference between each successive number.
Third row, write the difference between each number of the second row,
and so on until you find a pattern.

If differences don't work, I try divisions (dividing one number by the number to its immediate left)

For natural phenomenoms, I rarely have to go beyond 5 rows.

The pattern you propose appears to be a combination of two or more patterns (it certainly does not appear natural). You may have to extract one from the other, like undoing a zipper.

For example, the sequence:

1, 21, 2, 19, 4, 17, 8, 15, 16, 13, 32, 11, 64, 9, 128...

is an alternance of two sequences: 1, 2, 4, 8, 16, 32, 64, 128...
and 21, 19, 17, 15, 13, 11, 9...

In many cases, they are not that easy to separate.

It helps when you know what you are measuring. However, in class (or homework), you are often just given a string of numbers.

Answer 2

You can search for a pattern or rule that will generate the sequence of numbers you have, but if there is no such pattern, which I think is the case here, then you can only assume that the pattern is the current sequence itself which is now ready to repeat itself, so the next three numbers are 1,2,5.

Answer 3

You can find the formula to calculate next numbers, if you use matrix math (also called determination?).

The resulting formula will be like this:
y = a + bx^2 + cx^3 + dx^4 + ex^5 + fx^6 + gx^7 + hx^8 + ix^9 + jx^10
With a matrix, you can calculate a,b,c,d,e,f,g,h,i and j. I can't do that for you, i'm not that good in math. You'll have to study matrix math.

Answer 4

use this formula if its a regualr series

Ta=o+n(a+1)
where Ta is the number
o is the first number of the series
n is the difference between consecutive numbers
a is the position of number in the series

if its not regular u have to think cauz it can be a logical or object sequence too