# Simple recurring sequence (1, 2, 1, 2, 1, 2, 1, 2, )

1. Mar 31, 2010

### rekshaw

trivial yet my mind is blank, I'm wayyy overthinking this!

Was just thinking of a simple sequence to test-drive on my calculator, and this one came up in my mind (the sequence terms, not the sequence itself...)

I've been trying for the past hour to find a simbolic representation of a sequence that will spit out: 1, 2, 1, 2, 1, 2...

The farthest I got so far is to get it to give back 0, 2, 0, 2 with this:

$a_{n} = 1+(-1)^{n}$

From $$a_{1}$$ to $$a_{5}$$ it gives me: 0, 2, 0, 2, 0

I know it's probably the easiest thing in the world...

2. Mar 31, 2010

### Staff: Mentor

1.5+0.5=2, 1.5-0.5=1

3. Mar 31, 2010

### CRGreathouse

If you can find an expression for 0, 2, 0, 2, ... you should be able to find one for 0, 1, 0, 1, 0, .... If you can find one for 0, 1, 0, 1, 0, ... you should be able to find one for 1, 2, 1, 2, 1, ....

Alternately, it's a recurrence relation with a_{n+1} = 3 - a_n. You can find a second-order homogeneous recurrence relation if you prefer.

4. Mar 31, 2010

### dacruick

so they would be saying 1.5 + (0.5)(-1)^n

5. Mar 31, 2010

### rekshaw

Naturally! Thanks very much guys and sorry for the trivial question.