+939 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?
+130097 Call the first term a1 and the common difference, d
We gave these two equations
a1 + 22d = 1/4
a1 + 32d = 1/5 subtract the second equation from the first
-10d = 1/20
d = -1/200
To find the 43rd term :
a43 = a33 + 10d
a43 = a33 + 10 (-1/200)
a43 = 1/5 - 10/200
a43 = 1/5 - 1/20
a43 = 3/20
