Finding terms of sequence where a_{n+1} = |a_n| - 1

[Asla]

Homework Statement

Let a be a real number such that 1 < a < 2 ,{a_n} is a sequence defined by
a₁=a, a_n+1=|an|-1 (n=1,2,3...)
And put s_n=a₁+_a2+a₃+...a_n
i)Find the a₄,a₅,a₆,a₇
i)Find a₄,a₅,a₆,a₇

The Attempt at a Solution

I don't even know how to start.Maybe someone could give me an idea.

 

[haruspex]

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

 

[CompuChip]

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

 

[Asla]

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

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

 

[CompuChip]

Check your a₄.
|-0.75| - 1 = ... ?

 

[Asla]

Oh,..got it,.thanks.Okay

 

[CompuChip]

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