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

 Sep 30, 2018
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Nth term =F + (N - 1) x D, where F=First term, N=Number of terms, D=Common difference.
9 = F + (5 - 1) * D
-84 = F + (32 - 1) * D, solve for F, D
F =205/9 - First term
D =-31/9 - Common difference.
23rd term = 205/9 + (23 - 1) * -31/9
                      =205/9 - 682/9
                      =-477/9
                      =-53 - the 23rd term.

 Sep 30, 2018

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