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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 $27$th entry is $94$ and the $94$th entry is $27$. what's the first entry?



Answer :

Tutorconsortium423

The first entry is 94 + 26 = 120 since there are 26 entries after the 27th entry.

what is sequence ?

A sequence is a list of items that is in order in mathematics (or events). It has elements, just like a set (also called elements or terms). The length of the sequence is the total number of ordered items (potentially infinity).

Between the 27th and 94th entries, there are 67-1 = 66 entries, or 94 - 27 = 67. Entry 93 is 28, entry 92 is 29, etc., since entries before to the 94th entry were likely one greater than ones after it. Given that E93's value is 28, which is the average of E92 and E94, this makes sense.

If entry number 27 is 94, entry number 26 must be 95, entry number 25 must be 96, etc. The first entry is 94 + 26 = 120 since there are 26 entries after the 27th entry.

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