Answer
In each case, one possible answer is just the equation as presented (itisarecurrencerelationofdegree0). We will give an alternate answer.
Work Step by Step
a)One possible answer is an=an−1.
b) Note that an−an−1= 2n−(2n−2)=2. Therefore we have an=an−1+2 as one possible answer.
c) Just as in part(b), we have an=an−1+ 2.
d) Probably the simplest answer is an= 5an−1.
e) Since an−an−1=n2−(n−1)2= 2n−1,we have an=an−1+ 2n−1.
f) This is similar to part(e). One answer is an=an−1+ 2n.
g) Note that an−an−1=n+(−1)n−(n−1)−(−1)n−1= 1+2(−1)n. Thus we have an=an−1+1+2(−1)n.
h) an=nan−1
