The pattern {1, 3, 5, ...} is an arithmetic sequence with the following rule:
[tex]a_n = 1 + 2(n - 1)[/tex].
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
The pattern {1, 3, 5, ...} has first term and common difference given, respectively, by:
[tex]a_1 = 1, d = 2[/tex]
Hence the rule for the pattern is given by:
[tex]a_n = 1 + 2(n - 1)[/tex].
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
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