Find Formula for Repeating Sequence: 1 1 1 1 5 5 5 5 1 1 1 1

[dlthompson81]

Homework Statement

The sequence is 1 1 1 1 5 5 5 5 1 1 1 1

I need to find the formula for the sequence.

Homework Equations

The Attempt at a Solution

I had a previous problem that was similar. It was a sequence of 1 5 1 5 1 5. I managed to get it with the formula of 3+2(-1)ⁿ.

I did a little research through my notes/book and I found an explanation. It said I could set n equal to a fraction to get it to alternate numbers for different lengths. It was implying that (-1)^n/2 would give me 2 repeating of the number from the equation, (-1)^n/4 would give me 4 repeating, etc.

I understand the concept, at least, I think I do, but when I punch it into my calculator, (-1)^n/any# gives me an error. I know (-1)^n/# is the same as the # root of the number, and the root of -1 is an imaginary number.

Maybe I misunderstood something in the notes. Anyone point me in the right direction? Thanks.

 

[susskind_leon]

The hint with (-1)^(n/2) only works if you use the Gauss floor function, because, as you said correctly (-1)^(1/2)=i, hence not what you are looking for.

Try a+b*(-1)^n+c*(-1)^(2n)+d*(-1)^(3n)+e*(-1)^(4n)