## Meehan98 one year ago 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, ….

1. Meehan98

The choices are: $a _{n}=\frac{ n }{ 2n-1 }$ $a _{n}=\frac{ n }{ 2n+1 }$ $a _{n}=\frac{ 1 }{ 2n-1 }$ $a _{n}=\frac{ 1 }{ 2n+1 }$

2. anonymous

well.. it's asking, on "what pattern are the terms in the sequence show?"

3. Meehan98

Is the first step to figure out the first differences?

4. anonymous

to check what pattern is displaying

5. Meehan98

Okay, but they aren't constant differences.

6. zepdrix

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?

7. Meehan98

Thank you!