+864 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?
+1790 First, let's find the common rate of change through the arithmetic sequence. Let's let this be d.
From the problem, we can write the equation
\(1/4 + 10d = -1/5 \\ 10d = -1/5 - 1/4 = -9/20 \\ d = -9/200\)
Now, we can find the 43rd term of the sequence. We have
\(43rd term = -1/5 + 10d = -1/5 + 10 (-9/200) = -1/5 - 9/20 = -65/100 = -13 / 20 \)
So our final answer is -13/20.
Thanks! :)
