Sequences help?

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Answer 1 · 2018-04-20T16:14:08

#(a){1,0,0,...}#

#(b){-1,2,2,2,..}#

#(c)" " 2-sqrt2#

we have

#x_(n+1)=x_n^2-x_n#

#(a)" " x_1=1#

#:. x_2=x_1^2-x_1=1^2-1=0#

#x_3=x_2^2-x_2=0^2-0=0#

etc

sequence is

#1,0,0,0,..#

#(b)" " x_1=-1#

#x_2=x_1^2-x_1=(-1)^2-(-1)=1+1=2#

#x_3=x_2^2-x_2=2^2-2=4-2=2#

etc

#sequence is

#-1, 2,2, 2,..

#(c)" "x_1=1-sqrt2#

#x_2=x_1^2-x_1=(1-sqrt2)^2-(1-sqrt2)#

#=(1-sqrt2)[1-sqrt2-1]#

#=(1-sqrt2)(-sqrt2)#

#=2-sqrt2#