SOLUTION: What is the first 50 terms of a sequence whose 53th and 55th term are both 158?

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Question 974313: What is the first 50 terms of a sequence whose 53th and 55th term are both 158?


Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
What is the first 50 terms of a sequence whose 53th and 55th term are both 158?
If it is an arithmetic sequence then 

 and 

 and 

158+d = 158-d  since both equal a54
   2d = 0
    d = 0

Therefore all the terms are 158, that is, the sequence is

158, 158, 158, 158, 158, ...

------------------------------------

If it is a geometric sequence then 

 and 

 and 
                     

  since both equal a54




If r = 1, then all the terms are 158  
    
If r = -1, then the terms alternate between 158 and -158. With the
odd numbered terms being 158 and the even numbered terms being -158

So either way the sequence is either:

158, 158, 158, 158, 158, ...

or

158, -158, 158, -158, 158, -158, ...

Edwin

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