[Meekaboo2014]

4,-4,-9,-4,18,64...

[ebaines]

Hint: take the difference of pair of numbers in the sequence. Then take the differences of each pair of differences, etc. Eventually you'll come across a pattern that you can work backwards to find the next number. This technique works on any sequence that derives from a nth-order equation - in this case the underlying equation is a cubic.

[burgess87]

I tried to solve this puzzle but failed..
I am very excited to know this pattern..

Somebody please answer this question

[ebaines]

Starting with the sequence: 4, -4 , -9, -4, 18, 64

the differences bewtween each pair are:

A) -8, -5, 5, 22, 46

And the differences between these differences are:

B) 3, 10, 17, 24

Finally, the differences between these are:

C) 7, 7, 7

So - we conclude that the next number in series C is 7:

C) 7, 7, 7, 7

which means the next number in series B is 24+7=31:

B) 3, 10, 17, 24, 31

and the next numner is series A is 46+31 = 77:

A) -8, -5, 5, 22, 46, 77

Finally, the next number in the main sequence is 64+77 = 141:

4, -4, -9, -4, 18, 64, 141