Prove that every term of the sequence defined by b1=c b2=2c bk+1= 2bk+bk-1 is divisble by c?

prove that every term of the sequence defined by


b(1)=c


b(2)=2c


bk+1= 2bk+bk-1 is divisble by c


i know it's induction but i don't rember how exactly to prove it

Prove that every term of the sequence defined by b1=c b2=2c bk+1= 2bk+bk-1 is divisble by c?
Is there some part of the question you left out? This is, as you pointed out, a (generalized) induction argument:





Assume b_(k-1) and b_k are divisible by c, then 2b_k is divisible by c, so


b_(k+1) = 2b_k + b_(k_1)


is also divisible by c.





Since the induction assumptions are true for k=1,2, it is true for all positive integers k.
Reply:1) If a and b are both divisible by c, then a+b is divisible by c.


a = m*c, b = n*c, therefore (a+b) = (m+n)*c.





2) bk+1 = 2bk + bk-1


If bk and bk-1 are divisible by c, then bk+1 is also by 1).





3) b1 and b2 are divisible by c.





4) b3 is divisible by c by 2) and 3)


QED by induction.