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In an arithmetic sequence, the 23rd term is $\frac{1}{4},$ and the $33$rd term is $-\frac{1}{5}$. What is the $43$rd term?

 Aug 9, 2024
 #1
avatar+1918 
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First, we must figure out what the common difference in the arithmetric sequence is. Let's let that be d. 

From the problem, we have the equation

\(1/4 + 10d = -1/5 \\ 10d = -1/5 - 1/4 = -9/20 \\ d = -9/200\)

 

Now, we can use all the information we have to find the 43rd term. We have

\( -1/5 + 10d = -1/5 + 10 (-9/200) = -1/5 - 9/20 = -65/100 = -13 / 20\)

 

So our answer is -13/20. 

 

Thanks! :)

 Aug 9, 2024
edited by NotThatSmart  Aug 9, 2024

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