SOLUTION: A sequence Tn is defined by T1 = T2 = 1 and T(n+2) = T(n+1) + Tn Tn = {{{(a^n - b^n)/ sqrt( 5 )}}}, where a,b (a>b) are the roots of {{{x^2

SOLUTION: A sequence Tn is defined by T1 = T2 = 1 and T(n+2) = T(n+1) + Tn Tn = {{{(a^n - b^n)/ sqrt( 5 )}}}, where a,b (a>b) are the roots of {{{x^2 - x -1=0}}}. Assume the ratio {{{T

Question 1172425: A sequence Tn is defined by T1 = T2 = 1 and T(n+2) = T(n+1) + Tn
Tn = , where a,b (a>b) are the roots of .
Assume the ratio approaches a limit as n approaches infinity. Show that approaches
Answer by ikleyn(52771) (Show Source): You can put this solution on YOUR website!
.

See the link

https://www.nctm.org/tmf/library/drmath/view/52696.html

and find the solution there.

RELATED QUESTIONS
The Lucas numbers are defined by the recursive formula t1 = 2, t2 = 1, tn = tn - 1 + tn - (answered by Fombitz)

Tn=-4 T23=1 Tn=T(n-1)-3... (answered by ikleyn)