Solve the simultaneous recurrence relations with a0 = 1

Chapter 11, Problem 40E

(choose chapter or problem)

Solve the simultaneous recurrence relations

$a_{n}=3 a_{n-1}+2 b_{n-1}$

$b_{n}=a_{n-1}+2 b_{n-1}$

with $a_{0}=1$ and $b_{0}=-2$.

Equation Transcription:

${a}_{n}=3{a}_{n-1}+2{b}_{n-1}$

${b}_{n=}{a}_{n-1}+2{b}_{n-1}$

${a}_{0}=\ 1$

${b}_{0}=-2$

Text Transcription:

a_n=3a_n-1+2b_n-1

b_n=a_n-1+2b_n-1

a_0= 1

b_0= 2

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