We have #f(n)# an string;#ninNN# such that #f(n+1)-f(n)=3f(n)# and #f(0)=-1/2#.How to express #f(n)# according to #n#?

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Answer 1 · 2017-06-28T16:47:57

#f_n = -2^(2n-1)#

Making

#f_(n+1)-4f_n=0# with #f_0 = -1/2#

This is a homogeneous linear difference equation with generic solution

#f_n = c a^n#

Substituting we have

#c a^(n+1)-4ca^n = c(a-4)a^n = 0# so

#f_n = c4^n# but #f_0=c = -1/2# so finally

#f_n = -2^(2n-1)#