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There is a sequence of numbers such that every entry except for the first entry is the arithmetic mean of its two neighboring entries. The 27th entry is 94 and the 94th entry is 27 . What's the first entry?

Please answer quickly

 Dec 20, 2018
edited by Guest  Dec 20, 2018
edited by Guest  Dec 20, 2018
 #1
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94 =F + 26D,  
27 =F + 93D, solve for F, D
F =120 - First term
D = -1 - Common difference

 Dec 20, 2018
 #2
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It didn't say that it was an arithmetic sequence though. I am confused as to what you mean. Couldn't it have been any other kind of sequence?

Guest Dec 21, 2018
 #3
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Try solving it as Geometric sequence and see how far you get. You can try solving it an infinite series or Arithmetico - Geometric series and show the result. Remember evry term, except the first, is an arithmetic mean of its left and right terms.

Guest Dec 21, 2018
edited by Guest  Dec 21, 2018
 #4
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Thanks!

Guest Dec 21, 2018

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