# Homework Help: Sequence homework problem

1. Jun 19, 2013

### Asla

1. The problem statement, all variables and given/known data
Let a be a real number such that 1 < a < 2 ,{an} is a sequence defined by
a1=a, an+1=|an|-1 (n=1,2,3...)
And put sn=a1+a2+a3+....an
i)Find the a4,a5,a6,a7
i)Find a4,a5,a6,a7

3. The attempt at a solution
I don't even know how to start.Maybe someone could give me an idea.

2. Jun 19, 2013

### haruspex

Try to write out the first few terms of the sequence.

3. Jun 19, 2013

### CompuChip

Maybe try picking a concrete a, like a = 3/2 or a = 4/3, and see how the sequence behaves?

4. Jun 19, 2013

### Asla

Okay I took a=1.25,then got:
a1=1.25
a2=0.25
a3=-0.75
a4=0.25
a5=-0.75
a6=0.25
a7=-0.75
I then tried to interpret that to get that
a4 should be a-1 and a6 should be a-1 which are correct but for a5 and a7 I get the answer as 1-a for both but the answer should be a-2

5. Jun 19, 2013

### CompuChip

|-0.75| - 1 = ... ?

6. Jun 19, 2013

### Asla

Oh,..got it,.thanks.Okay

7. Jun 19, 2013

### CompuChip

OK now can you do it more generally, for a = 1 + r, where 0 < r < 1?