builder method B = {2, 5, 8, 11, 14, 17, 20}

Question

Rewrite the following set using the set builder method: B = {2, 5, 8, 11, 14, 17, 20} my answer is
B={x:x∈Z where x is addition of 3 ,and-1 ≤ x ≤ 17}

Answer 1

A concise way of writing your set is the following:

B= {$3n-1: n\leq7$ and $n\in\mathbb{N}$}. Do you see why?

Edit:

Note that the given set of numbers forms an arithmetic progression: any consecutive two terms/numbers have the exact same (common) difference. In this case, the difference is $3$. If you have an arithmetic progression with the first term $a$ and the common difference $d$, then it's $n$th term can be written as $a+ (n-1)d$. What's $a$ and $d$ in your case? Then you get your $n$th term of the arithmetic progression/sequence. Also, think about why I chose $n\leq7$ ?

Answer 2

Hint: This is a finite arithmetic sequence, so you could specify the first term $a$, the difference $d$, and maximum number $N$ of additional terms. The generic term then could be of the form $a+nd$ for an appropriate range of $n$.