Subject: discrete mathematics the level of the question - college who is asking the question - student Hi! I'm having a lot of trouble with this question. A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck-3 for all integers Prove that cn is even for all integers. This is what I have done so far: cn=5cn-3 Let n=k where k belongs to all integers ck=5ck-3 (Induction Hypothesis) Let n=k+1 ck+1=5ck+1-3 ck+1=5ck-2 ck+ck+1=5ck-2 (by Induction Hypothesis) 5ck-3+ck+1=5ck-2 This is where I am stuck...I'm not sure.. I might actually be going about this problem completely wrong since it says that you need to prove cn is even. Can you help me? =/ Thank you very much!! Hi, We think that you may be reading the question incorrectly. You are to show that cn is even for all integers where c0 = 2 c1 = 4 c2 = 6 and for all k larger than or equal to 3, ck = 5 ck-3 You are probably best to use "Strong Induction" for this sequence. In this case, your induction hypothesis should read: "assume ck is even for all natural numbers k such that 0< = k < n" Your final step is to show that cn is even using the definition of the sequence, i.e. If n >= 3, cn = 5cn-3 will be even because cn-3 will be even by our induction hypothesis. Your basic step took care of the case where n = 0, 1 and 2 and we have successfully proved the result is true for all n >= 3. Hope this helps, Leeanne and Penny Go to Math Central