Quandaries and Queries


I am a high school teacher (9-12) and have the following question.
Solve this recurrence relation, with the initial conditions.
A1 = 10
A2 = 100
An = 10a n-1 + 29a n-2


Becky, this seems a bit tough for high school.

To solve a linear recurrence like you have (An - 10A n-1 - 29An-2 = 0) you
need to look at its characteristic equation x2-10x-29 = 0 and find its
roots. Call then s & t. Then An looks like p(sn) + q(tn) where p & q are
constants determined by the initial conditions, A1 = 10 and A2 = 100.
In your case the roots s & t are not very nice to work with:
(10+/- Sqrt(216))/2.

The dominant term in your solution should be the p((10+Sqrt(216))/2)n term.


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