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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 46. What's the first entry?

 Aug 29, 2021
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94 ==F + 26D,   

46==F + 93D, solve for D, F

 

Use substitution to get:

 

F==7546 / 67 - this is the first term

D== - 48 / 67 - this is the common diffrence.

 

Your sequence looks like this:

7546 / 67 , 7498 / 67 , 7450 / 67 , 7402 / 67 , 7354 / 67 , 7306 / 67 , 7258 / 67 , 7210 / 67 , 7162 / 67 ...etc.

 Aug 29, 2021

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