What is the next number in this sequence 7 9 12 16?

Answer 1

The first thing to do when tackling a sequence is note the differences between the values. In this case they are 2, 3, 4

As they are not equal, we look at the differences of the differences:

1, 1

These are equal, so the equation for the sequence begins x2/2

The sequence minus x2/2 is 6.5, 7, 7.5, 8

The differences in this new sequence are 0.5, 0.5, 0.5

Thus the equation continues x2/2 + x/2

The sequence minus x2/2 + x/2 is 6, 6, 6, 6

Thus the entire equation is x2/2 + x/2 + 6, or more simply (x2+x+12)/2

Using this equation you can find the next few numbers of the sequence:

21, 27, 34, 42, 51...