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According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.
The simplest rule is un = 18 - 3n
Each term is derived from previous term by subtracting 3, so the sequence is 15 12 9 6 3 0 etc
15 is 1st term
12 is 2nd term and 12 = 15 - 3(1)
9 is 3rd term and 9 = 15 - 3(2)
6 is 4th term and 6 = 15 - 3(3)
so the Nth term is 15 - 3(N-1)
eg if N=6 then the 6th term is 15 - 3(5) = 15 - 15 = 0
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I'm seeing a lot of confused, uneducated answers. Here's the answer you want:
-3n + 18
or
-3(n - 1) + 15
To find the formula for an arithmetic sequence/series, use the formula d(n-1) + a, where d is the common difference (in this case, each term is 3 LOWER than the last, so d=-3) and a is the first term in the sequence (in this case, a = 15)
This gives us -3(n - 1) + 15
= -3n + 3 + 15
= -3n + 18
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