Who is asking: Student Level: Secondary Question: A sequence s is defined recursively as follows: s0=1 s1=2 sk=2sk-2 for all integers - Compute s2,s3,s4... to guess an explicit formula for the sequence sk. s2=2(s2-2)=2(s0)=2(1)=2 s3=2(s3-2)=2(s1)=2(2)=4 s4=2(s4-2)=2(s2)=2(2)=4 I understand how to compute it, and I see the pattern is 1,2,2,4,4,8,8...and so on, but I am having trouble figuring out the formula... - Prove (through Induction) that the formula you obtained previously is correct. If you could help me with this problem, I would very much appreciate it!!! Thank you Hi, You're right about the sequence and you should notice also that the numbers are powers of 2 so your problem is to find an f(n) such that for your nth term sn = 2f(n). Look at n= 3 & 4; you need 22 in both cases. Look at n= 5 & 6; you need 23 in both cases. Look at n= 7 & 8; you need 24 in both cases. That is 3 & 4 correspond to 2; 5 & 6 correspond to 3; 7 & 8 correspond to 4; etc. Doesn't the required exponent look about 1/2 of n? You might want to look at the integer part of (n+1)/2. Penny Go to Math Central