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) About Me  (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 

a%5B53%5D%2Bd=a%5B54%5D and a%5B54%5D%2Bd=a%5B55%5D

158%2Bd=a%5B54%5D and a%5B54%5D%2Bd=158%7D%7D%0D%0A+++++++++++++++++++++%7B%7B%7Ba%5B54%5D=158-d

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, ...

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If it is a geometric sequence then 

a%5B53%5Dr=a%5B54%5D and a%5B54%5Dr=a%5B55%5D

158r=a%5B54%5D and a%5B54%5Dr=158
                     a%5B54%5D=158%2Fr

158r+=+158%2Fr  since both equal a54
158r%5E2=158
r%5E2=1
r=%22%22+%2B-+1

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