Math CentralQuandaries & Queries


Question from jarred, a student:

i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time.


There is an on-line resource that explores integer sequences:
One interesting observation is that A recursive formula may not be unique. Some may be simpler than others, but there must be a number of them (which will give different number values as you go further out). The site gives 95 answers for your numbers!

All of that said, there is a simpler set of numbers which is probably was in the experience of the person who gave you this assignment. To find the formula, try taking first differences:

3   6   10   15   21
  3   4   5   6  

and perhaps second differences:

3   6   10   15   21
  3   4   5   6  
    1   1   1    

These match the first of the 95 answers on the site I mentioned.
As a project, try looking at the bigger ideas for which this is an example.

Walter Whiteley


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