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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
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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=1/510d=1/51/4=9/20d=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)=1/59/20=65/100=13/20

 

So our answer is -13/20. 

 

Thanks! :)

 Aug 9, 2024
edited by NotThatSmart  Aug 9, 2024

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