Let a be a real number...?
Let 'a' be a real number such that a 1 < a < 2. a(sub n) is the sequence defined by:
a1 = a,
an+1 = |an| -1
n= 1,2,3......
And put Sn= a1+a2....+an
Find. a4, a5 a6 a7
Find S2, S4, S6
I'm not following the problem at all O.o
the answers are a4 = 1-a
a5 = a -2
a6 = 1 -a
a7 = a-2
Maybe if i just get an example to solve a4 I might be able to figure out the rest...
The recursive relation defining the sequence can be written as...
(1)
The function f(x) is illustrated here...
There is only one 'attractive fixed point' in and, because f(x) crosses the x axis with slope -2 any initial value a will produce a sequence asyntotically oscillating around - 1/2. Regarding the 'sum' is...
(2)
Kind regards