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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?

 Jun 16, 2024
 #1
avatar+129733 
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 {   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

 

cool cool cool

 Jun 16, 2024

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