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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 39. What's the first entry?

 Dec 27, 2021
 #1
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Take a look at this: https://web2.0calc.com/questions/sequences_7

 Dec 28, 2021
 #2
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There is a mistake in your question! The 94th term ==27 NOT 39 !! Check your numbers carefully.

 

94==F + 26D,   

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

 

F ==120 - this is the first term

D == - 1 - this is the common difference.

 

Your sequence looks like this:

 

120 , 119 , 118 , 117 , 116 , 115 , 114 , 113 , 112 , 111 , 110 , 109 , 108 , 107 , 106 , 105 , 104 , 103 , 102 , 101 , 100 , 99 , 98 , 97 , 96 , 95 , 94 , 93 , 92 , 91 , 90 , 89 , 88 , 87 , 86 , 85 , 84 , 83 , 82 , 81 , 80 , 79 , 78 , 77 , 76 , 75 , 74 , 73 , 72 , 71 , 70 , 69 , 68 , 67 , 66 , 65 , 64 , 63 , 62 , 61 , 60 , 59 , 58 , 57 , 56 , 55 , 54 , 53 , 52 , 51 , 50 , 49 , 48 , 47 , 46 , 45 , 44 , 43 , 42 , 41 , 40 , 39 , 38 , 37 , 36 , 35 , 34 , 33 , 32 , 31 , 30 , 29 , 28 , 27 , 26 , 25 , 24 , 23 , 22 , 21 , >>Number of terms = 100>>Total Sum == 7050

 Dec 28, 2021

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