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I can find the nth term of any quadratic sequence by finding a (e.g.) second difference (Example 1 below). My question is how to find the nth term for a sequence that has (e.g.) n to the -1 or n to the -2 in its nth term (that is unknown at first)(example 2). I have tried to use google but found irrelevant results.

Example 1

3, 9, 19, 33

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6 10 14

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4     4

4=2a a=2 So 2n squared is used. Take away 2n squared etc. ... End up with 2n squared + 1.

Example 2

1/1, 1/2, 1/3, 1/4 etc

I know the nth term is 1/n but what's the 'official' process?

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1 Answer 1

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There is no "official" process. There is no single approach that can give you the expression for the $n$th term of sequences. There is just a long list of techniques which work some times, and when they don't you start guessing.

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