SOLUTION: I am trying to find the explicit formula for the following sequence: -2 1/2, -2, -1 1/2, -1, -1/2 In this problem, -2 1/2 corresponds to the term 1, -2 corresponds to the ter

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Question 196139: I am trying to find the explicit formula for the following sequence:
-2 1/2, -2, -1 1/2, -1, -1/2
In this problem, -2 1/2 corresponds to the term 1, -2 corresponds to the term 2, -1 1/2 corresponds to the term 3, and so on. I've been working on this problem for over an hour and have tried lots of different formulas, but none work. Please help.
Thank you so much.
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Have you tried:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Edwin's solution:
, , , , ,...

It is an arithmetic sequence because obviously  is 
being added to each term to get the next term.  Therefore
the common difference is .

The th term of an arithmetic sequence is given by the
formula:



So, upon substituting:



Change the mixed fraction  
to the improper fraction 



Multiply through by 2 to clear of fractions:







Divide both sides by 2

 

Edwin
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