Is a(n) bounded by a(1)*c^(n-1)?

[transgalactic]

i am given a real and positive number a1 a2 a3 ...
which goes by a(n)<=c*a(n-1) for every n=>2 for a certain given number c>0 .

prove that
a(n)<=a(1)*c^(n-1)

??

a(n) is the n'th number of the series

 

[nicksauce]

Use a proof by induction. It should be fairly straight forward.

 

[transgalactic]

i don't have a base case here

and there are two variables

??

 

[VeeEight]

Use induction of n. Your base case would be n=2.

 

[transgalactic]

for n=2
i get
a(2)=c*a(1)

this base case doesn't prove anything

??

 

[nicksauce]

The base case is trivially true, since it is the same condition for the members of the sequence.