Practice!

Sample Problem

Is the sequence (with a1=0 and an=an-1-n)

Solution

a1=0

a2=a1-2=0-2=-2

a3=a2-3=-2-3=-5

a4=a3-4=-5-4=-9

a5=a4-5=-9-5=-14

First differences=-2, -3, -4, -5…

Second differences=-1, -1, -1…

For this sequence, since the second differences are all the same, the sequence has a perfect quadratic model. (if the first differences were to be all the same, the sequence has a linear model)