A Sequence of Events

A sequence is a succession of numbers that follow on from one another.

The simplest is

1, 2, 3, 4, 5, 6.....

Where all you do to get the next is add 1 to the last.

2, 4, 6, 8, 10....

is similar, in that you add 2 to the last one.

1, 3, 5, 7, 9....

is also similar, adding 2, but starting at a different number.

So much for addition.

How about 1, 2, 2, 4, 8, 16, 32....

This one is where you multiply the previous two to get the next.

Or even,

1, 2, 3, 5, 8, 13, 21, ......

where you add the previous 2 to get the next.

And so it goes on.

So, a common puzzle is to guess what the next one is....

Try this..

1, 4, 9, 16, 25....?

The answer is of course 36, each being the square of the integers.

This one..

1, 8, 27, 64....

The answer is 125, since they are the cubes of integers.

What about this one?

3, 3, 5, 4, 4, 3, 5, ?

That's harder - the answer is 5, the numbers being the "number of letters" in the integers. ONE = 3, TWO = 3, THREE = 5 etc

NOW, try THIS one...

1, 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 11, ?

What is next? First prize is a can of worms