Let the next 3 terms be x, y and z.
The given sequence would be
4, 10, 14, 24, 38, 62, x, y, z
let us examine the pattern below
14 - 4 = 10
24 - 10 = 14
38 - 14 = 24
62 - 24 = 38
Thus,
x - 38 = 62
x = 62 + 38
x = 100
then,
y - 62 = 100
y = 100 + 62
y = 162
Finally,
z - 100 = 162
z = 162 + 100
z = 262
Thus, the next three numbers are 100, 162 and 262