The pattern {1, 3, 5, ...} is an arithmetic sequence with the following rule:
[tex]a_n = 1 + 2(n - 1)[/tex].
What is an arithmetic sequence?
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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