How can I put A={1,4,7,10,13,16,19,22,25,28} in set builder notation. I just learned this and can't figure it out.

notice all the numbers are 3 apart

so the formula to generate the numbers would be
3n - 2, where n ∈ N0

so

A = { 3n-2 | n ∈ N0 , n ≤ 10 }

I just noticed that I wanted the n's to start at 1, not at 0

so change it to

{......| n ∈ N ......}

To express the set A={1,4,7,10,13,16,19,22,25,28} in set builder notation, you need to identify the pattern or rule that defines the elements in the set.

Looking at the given set, we can observe that each element is obtained by adding 3 to the previous element. Therefore, the pattern can be stated as: "Start with 1, and add 3 repeatedly."

Using this pattern, we can rewrite the set A in set builder notation as:

A = {x | x = 1 + 3n, where n is a non-negative integer}

In set builder notation, the set is represented as "A" followed by a vertical line "|" which reads as "such that." Then, we define the rule or pattern that the elements of the set must satisfy. In this case, "x = 1 + 3n" defines the rule, where "x" represents the elements of the set, and "n" denotes a non-negative integer used to generate elements.

Therefore, the set A can be expressed in set builder notation as {x | x = 1 + 3n, where n is a non-negative integer}.