let-x-n-be-a-sequence-with-x-0-2-and-x-1-7-and-x-n-1-7x-n-12x-n-1-Find-the-general-term-of-x-n-

Question Number 90217 by Maclaurin Stickker last updated on 22/Apr/20

l e t x_{n} b e a s e q u e n c e w i t h x_{0} = 2 a n d x_{1} = 7

a n d x_{n + 1} = 7 x_{n} - 12 x_{n - 1} .

F i n d t h e g e n e r a l t e r m o f x_{n} .

Commented by jagoll last updated on 22/Apr/20

p^{2} - 7 p + 12 = 0

p = 3 \land p = 4

x_{n} = A . 3^{n} + B . 4^{n}

n = 0 \Rightarrow 2 = A + B

n = 1 \Rightarrow 7 = 3 A + 4 B

B = 1 \land A = 1

∴ x_{n} = 1 . 3^{n} + 1 . 4^{n} = 3^{n} + 4^{n}

Commented by Maclaurin Stickker last updated on 22/Apr/20

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