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## Main Question or Discussion Point

What are some of the methods of finding the general term of a sequence of numbers? for a sequence from n = 1 to n = 6 such as:

1, 3, 6, 10, 15, 21

the general term is:

n(n+1)/2.

This is relatively easy to find using guess and check, however I was wondering if there was a general algorithm one could use to find the general term for a more complicated series such as:

3, 3, 15, 45, 99, 183.

The general term for that series is:

n^3 - 7n + 9

however I obviously reverse engineered that sequence. Finding the general term from the sequence of numbers for a complicated geometric sequence such as the one above seems daunting yet possible.

I would also like to know what branch of mathematics this question would fall under. I did a google search for series and sequences and found this forum, however not an answer to my question. Again, please discuss some of the best methods for finding the general term of a sequence or series from the numbers of the sequence. (a series is the summation of the values of a sequence)

1, 3, 6, 10, 15, 21

the general term is:

n(n+1)/2.

This is relatively easy to find using guess and check, however I was wondering if there was a general algorithm one could use to find the general term for a more complicated series such as:

3, 3, 15, 45, 99, 183.

The general term for that series is:

n^3 - 7n + 9

however I obviously reverse engineered that sequence. Finding the general term from the sequence of numbers for a complicated geometric sequence such as the one above seems daunting yet possible.

I would also like to know what branch of mathematics this question would fall under. I did a google search for series and sequences and found this forum, however not an answer to my question. Again, please discuss some of the best methods for finding the general term of a sequence or series from the numbers of the sequence. (a series is the summation of the values of a sequence)