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The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?

 

BTW the answer is not 40

 Jul 27, 2020
 #1
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from 5th term to 32 term is  27 d

  9 + 27 d  = -84

               d = -3.1111111        or   (- 93/27)

 

 

*** edited ***

 

 

From 5th term to 23rd is 18 d

 

9 + 18 (-93/27) = - 53

 Jul 27, 2020
edited by ElectricPavlov  Jul 27, 2020
edited by ElectricPavlov  Jul 30, 2020
 #2
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F = First term

D = Common difference

 

9 = F + 4D, 

-84 =F +31D, solve for F, D

F =205 / 9

D = - 31 / 9

 

23rd term =205/9 + (-31/9) * (23-1)

                  =205/9  -(31/9) *22

                  =205/9 - 682/9

                  = - 477 / 9

                  = - 53

 Jul 28, 2020
edited by Guest  Jul 28, 2020

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