Number pattern help please?

Question

i can't figure out this number pattern...

1, 6, 15, 44, 109...

what is the next number?

Answer 1

Sorry for the late reply

So the increment between numbers go

5  9  29  65

To find the next increment, add ( 4*previous increment ) to the current increment.

So,

5+ 4x1 = 9 ( assuming the first increment was 1 because 0 -> 1 )

9+ 4x5 = 29

29+ 4x9 = 65

The next increment would be

54+ 4x29 = 170

The next number is 109 + 170 = 279

Answer 2

That's a difficult one.  You don't have much to go by, either.  The most pattern I see is:

1 (x 2 + 2) 6 (x 2 + 3) 15 (x 2 + (7x2)) 44 (x 2 + (7x3))

Answer 3

Arrange the numbers in a column with a line between each one:

1

6

15

44

109

Then work out the difference between each pair of adjoining numbers and write it in a new column with the answer on the in-between lines:

[I have tried to do this here but it won't print in columns. Sorry]

You then work out the difference between each pair of adjoining numbers in the new column and repeat the process until you see a pattern appearing in a column. You end up with a sideways pyramid.

You can see that the 4th column is always 16 so if you work backwards by adding numbers, you make an extra diagonal layer of numbers at the bottom:

Sooooo, the next number in the series is 226. And after that comes 411 and the one after that is 680, followed by 1049

It's great fun once you know the technique!