The next number in the pattern would be 14.03.
To find this, note the differences found by subtracting each number from the number that comes after.
4.03 - 2.78 = 1.25
5.78 - 4.03 = 1.75
8.03 - 5.78 = 2.25
10.78 - 8.03 = 2.75
Since each difference goes up by .5 each time, we know we can add .5 to the last difference to find the newest one.
2.75 + .5 = 3.25
Now we have the difference, so we add that to the last number.
10.78 + 3.25 = 14.03
