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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?

 Jul 8, 2024
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In order to know what the 43rd term is, we must know the common difference. 

Luckily, the problem basically tells us what the difference is. 

Let's let that difference be d. We have from the problem that

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

 

Now, we biuld off of the 33rd term. Since we know it is 1/5, we simply just have to add the d a number of times. 

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! :)

 Jul 8, 2024

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