[A] Question 6: Intermediate Algebra

Algebra Level 3

Some might find this familiar.

Given that x n + 1 = x n 1 2 n x n { x }_{ n+1 }={ x }_{ n-1 }^{ 2 }-n{ x }_{ n } , x 0 = 3 , x 1 = 4 { x }_{ 0 }=3,\quad { x }_{ 1 }=4 ,

find x 982 { x }_{ 982 } .

Extra:

Find the general term for x n { x }_{ n } .


The answer is 985.

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1 solution

Zi Song Yeoh
Sep 18, 2014

One can show by induction that in fact, x n = n + 3 x_n = n + 3 . Thus, x 982 = 985 x_{982} = \boxed{985} . (Sorry, I'm omitting the details of the calculation here.)

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