Can someone explain to me how to do this, please! This lesson really confused me. Identify a possible explicit rule for the nth term of the sequence 1, 1/3, 1/5, 1/7, 1/9, ….

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Can someone explain to me how to do this, please! This lesson really confused me. Identify a possible explicit rule for the nth term of the sequence 1, 1/3, 1/5, 1/7, 1/9, ….

Mathematics
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The choices are: \[a _{n}=\frac{ n }{ 2n-1 }\] \[a _{n}=\frac{ n }{ 2n+1 }\] \[a _{n}=\frac{ 1 }{ 2n-1 }\] \[a _{n}=\frac{ 1 }{ 2n+1 }\]
well.. it's asking, on "what pattern are the terms in the sequence show?"
Is the first step to figure out the first differences?

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to check what pattern is displaying
Okay, but they aren't constant differences.
First, think about your sequence like this:\[\large\rm \frac{1}{1},~\frac{1}{3},~\frac{1}{5},~\frac{1}{7},...\]If you rewrite the first number like that, it might help you to see what is going on. They are all `odd` denominators. \(\large\rm 2n-1\) and \(\large\rm 2n+1\) are two ways of writing odd numbers. Check out \(\large\rm 2n+1\). If we start counting from n=1, 2(1)+1=3 2(2)+1=5 2(2)+1+7 How bout the other one? \(\large\rm 2n-1\). Again if we start counting from n=1, 2(1)-1=1 2(2)-1=3 2(3)-1=5 Hmm these second set of numbers seem to match our denominators, yes?
Thank you!

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