SOLUTION: 3 6 17 42 87 158 find the sequence

Algebra ->  Sequences-and-series -> SOLUTION: 3 6 17 42 87 158 find the sequence       Log On


   

Question 995748: 3 6 17 42 87 158 find the sequence

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Find the common difference:
   3     6     17     42     87    158
    \   / \    / \    / \    / \    / 
      3     11     25     45     71
       \    / \    / \    / \    / 
          8     14     20     26
           \    / \    / \    /
              6      6      6

The actual difference numbers don't matter. The important thing is that the differences are the same in the third row of differences. Hence, the sequence can be modeled with a 3rd-degree polynomial.



The value of the function at is ,

Hence



Or, more simply put



Then, when , . Similar to above we derive:



In a like manner we can derive:



And



Solve the 4X4 system of linear equations to find the coefficients of the 3rd-degree polynomial that models your desired sequence.

John

My calculator said it, I believe it, that settles it