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

\ / \ / \ /

6 10 14

\/    \/

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?


1 Answer 1


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.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .