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# arithmetic sequence

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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