Hi Forum!

I'm having difficulties with absolute value numbers.

This sequence is kind of strange, take a look:

Let a be a Real number such that 1<a<2, the sequence {an} is defined by

a1=a and an+1= |an|-1 such that {n=1,2,3,4,...}

And granted that Sn=a1+a2+a3+...+an.

--Find a4, a5, a6 and a7

Ok, no problem with this one

a2=|a1|-1 a2+1=|a1| a1=-a2-1 a2= -a+1

a3=|a2|-1 a3+1=|-a+1| -a3-1=-a+1 a3= a-2

a4=|a3|-1 a4+1=|a-2| -a4-1=a-2 a4= -a+1

...

So, there's an alternate sequence between odd numbered and even numbered terms.

a4=-a+1 a5=a-2

a6=-a+1 a6=a-2

For the problematic part:

Find S2,S4 and S6

S2=a1+a2

S2=a+(-a+1) = 1

But real answer is 2a-1

So, what's wrong Forum?

I really don't get what is wrong on this one.

If someone has some tips for the absolute value part, I would humbly accept it.

Thanks