# Sequence possibilities

Why is it impossible to know the next number in a sequence with two numbers for you?

My friend asked me 1, 2 , what comes next?

1, 2, n

The answer could be any number, because

all the information displayed is that 2-1=1, but we know that the result, 1 is not enough to tell us what the next gap should be.(If we add that gap to the two it will give us are next.)

We could make this n-2 which is the difference, then we add the 2 in the sequence , this can be shown as n-2+2=n, this doesn't show information but proves it's impossible to get it wrong or right.

If we have three numbers it's a little more possible

Say 1, 2, 4. Now we can make out a little more. We see that 2-1=1, and that 4-2=2, since the differences follow the sequences numbers we know it's doubling (or adding one more each time) so we can predict the next number by doubling four, which is eight, so know we know the pattern is doubling, and the sequence goes 1, 2, 4, 8...