There are infinitely many pattern rules. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question followed by any number that you choose to be the next one. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest solution, based on a polynomial of order 3 is
t(n) = 1.5*(-n^3 + 12n^2 - 26n + 21) for n = 1, 2, 3, ...
from 12 to 16 is 4 then from 16 to fiftine is one then from15-19 is 4 so one so forth one is +4 the next is -1
4*2-2=6 6*2-2=10
The rule of this pattern is -2 + 6 +4 so the next number would be 16.
The rule is multiply the previous term by -1 to find the next term.
5-30-6-42-7-56-8-72
Multiply each preceding term by 4.
from 12 to 16 is 4 then from 16 to fiftine is one then from15-19 is 4 so one so forth one is +4 the next is -1
Double the previous number
consecutive square numbers
r=5>7}2
4*2-2=6 6*2-2=10
The rule of this pattern is -2 + 6 +4 so the next number would be 16.
The rule is multiply the previous term by -1 to find the next term.
5-30-6-42-7-56-8-72
To guess a rule for a pattern, you need several numbers, not just one. Of course, you can invent any rule, for example, "all numbers in the sequence are equal to -4", or some more complicated rule.
The pattern will be +2, +3, +4, +4
1, 4, 9, 16, ......., (n squared),