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The first and ninth terms of an arithmetic sequence are 2/3 and 4/9, respectively. What is the fifth term?

 Oct 8, 2020
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 The 5th term is \(\frac{5}{9}\) . Here's my methodology:

 

To find the 5th term, we have to first find the difference between each of the terms. Since adding the difference 8 times to the 1st term gives us the 9th term, we can set up the equation \(\frac{4}{9}-\frac{2}{3}=8x\).

 

We can then solve for x to get \(x=-\frac{1}{36}\)

 

Then, all we have to do is add \(4x\)  to the 1st term to get \(\frac{2}{3}-\frac{5}{36}=\frac{24}{36}-\frac{4}{36}=\frac{20}{36}=\boxed{\frac{5}{9}}\).

 

I hope this helps!

 

–Doggo

 Oct 8, 2020

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