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

 Mar 26, 2022
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If the first term of an arithmetic sequence is a and the common difference is d,

then the fifth term is:  a + 4d  and the 32nd term is:  a + 31 d.

 

We have these equations:  a +    4d  =  9

                                            a + 31d  =  84

 

Solving, we have:                       27d  =  75     --->    d  =  75/27  =  25/9

 

which makes:                                  a  =  -19/9

 

To find the 23rd term:  a + 22d  =  -19/9 + 22(25/9)  =  ...

 Mar 26, 2022

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