GIVEN F12 F24 F38 F414 F522 F632 USE THE METHOD DIFFERE

GIVEN: F(1)=2 , F(2)=4 , F(3)=8 , F(4)=14 , F(5)=22 , F(6)=32.

USE THE METHOD DIFFERENCES TO FIND THE POLYNOMIAL REPRESENTING F(N).

This is a question from my discrete math class.

Solution

N = 1 2 3 4 5 6

F(N) =2 4 8 14 22 32

D\' = 2 6 6 8 10

D\" = 4 0 2 2

D\'\'\' = 4 2 0

D\'\'\'\' = 2 2

Because the constant appears at 4th difference, WE CONCLUDE THAT OUR EQUATION IS OF FOURTH ORDER.