SOLUTION: Describe the long term behaviour of the sequence (xn) given by xn = 11x(0.9)n -5 (n=1,2,3,…) Justify answer. xn should read x to the base n and 0.9 should to be to the powe

Algebra ->  Trigonometry-basics -> SOLUTION: Describe the long term behaviour of the sequence (xn) given by xn = 11x(0.9)n -5 (n=1,2,3,…) Justify answer. xn should read x to the base n and 0.9 should to be to the powe      Log On


   



Question 1043973: Describe the long term behaviour of the sequence (xn) given by
xn = 11x(0.9)n -5 (n=1,2,3,…)
Justify answer.
xn should read x to the base n and 0.9 should to be to the power n - sorry, can't seem to do this action on my keyboard
I have muddled through a bit thinking every term is obtained by multiplying by 0.9 but think I'm going in the wrong direction.
Help!!!!!
Thanks

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You are saying with your description,
x[n]=11x(0.9)^n-5
which when given the rendering tagging will show as x%5Bn%5D=11x%280.9%29%5En-5.
You do not yet have your formula right.

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You gave no indication what you want with the variable factor, x, on the right hand member of the formula. Explain it logically or fix it if you want help.

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SO You really have this: highlight_green%28x%5Bn%5D=11%280.9%29%5En-5%29.
Your goal is to find what x%5Bn%5D tends to, as n tends toward the right without end. You can figure how that will work. 0.9 is near 1 but a little smaller; 0.9*0.9, or being n=2, is a smaller factor than 0.9; and 0.9*0.9*0.9 for n=3, becomes still smaller a factor. What is the factor when n=12? What is the factor when n=85? What happens to the TERM, 11%2A%280.9%29%5En? You should be able to understand where this is going....

As n gets increasingly big, x%5Bn%5D approaches but never reaches 0-5.