Given any number it is easy to find a rule based on a polynomial of order 5+k such that the first five numbers are as listed in the question and the next k are the given "next" numbers.
However, use the rule
Un = (-6n4 + 83n3 - 411n2 + 874n - 468)/6
Accordingly, the next three numbers are 22, -71, -310
The next two numbers in the sequence are... 45 & 54.
The least common multiple of the numbers 12 and 34 is 204.
You are given the minimum 28 and maximum 34, which means that all the numbers are in the set (28, 29, 30, 31, 32, 33, 34). Since there are fewer than 12 numbers in the set to choose from, there will have to be repeats. You are given the mode 29, which means that 29 appears more often than any other number in the set. The median is 30, which means that half the numbers are above 30 and half are below. There are many different ways to construct a set meeting those conditions. One such set would be (28, 29, 29, 29, 29, 30, 30, 31, 32, 33, 34, 34).
16 is the whole set
The next four composite numbers after 30 are 32, 33, 34 and 35.
First, add all the numbers. Next, divide the sum by how many numbers there were. Example: 34 + 23 12 ----------- 69 69 divide by 3 is ... 23: That is your average.
12 and 22.
There are an infinite set of numbers whose average is 34. {33, 35} {33, 34, 35} {33, 33, 35, 35} {1, 1, 1, 133} These are just a few examples.
The mode of the set of numbers {31, 34, 34, 35, 36} is 34, as it is the number that occurs the most.
58
23 and 11
12 and 22