+782 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?
+129839 { an = n* a1 + (n) (n-1) / 2 * d }
23a1 + 253d = 1/4 mult through by 33 → 759x + 8349y = 33/4
33a1 + 528d = - 1/5 mult through by -23 → 759x - 12144y = 23/5
Add these
-3795d = 257 / 20
d = -257 / 75900
23a1 + 253 (-257/75900) = 1/4
a1 = 83 /1725
a43 = 43(83/1725) + 903(-257/75900) = -15007 / 15180
