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

 Jun 26, 2020
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Use the equation for a term of an arithemetic sequence: a+d(n-1), where a is the first term, r is the common difference, and n is the term you are trying to find the value of.

 

From the first sentence we form the equation:

a+d(4)=9--->a+4d=9

a+d(31)=-84--->a+31d=-84

 

Now we have a system of equations and solve to get a=205/9 and d=-31/9.

 

So the 23rd term is

205/9-31/9(23-1)

=205/9-31/9*22

=-53

 
 Jun 26, 2020

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