Explore BrainMass
Share

Algebra: Simultaneous Recurrence Relations

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Solve the simultaneous recurrence relations given below.

a(n) = 3a(n-1) + 2b(n-1)
b(n) = a(n-1) + 2b(n-1)

a(0) = 1
b(0) = 2

© BrainMass Inc. brainmass.com March 21, 2019, 9:10 pm ad1c9bdddf
https://brainmass.com/math/recurrence-relation/algebra-simultaneous-recurrence-relations-364825

Attachments

Solution Preview

We have the following system:

Firstly, we'll subtract the second equation from the first one, and get:
(1)
Now, if we put n-1 instead of n, we'll get:
(2)

Then, from the first equation, we'll subtract from both sides, and get:
- = 2( - ) (3).

And now we'll substitute (2) in (3) and get:
- = 4 , which is same as ...

Solution Summary

The expert solves a system of two recurrence sequences.

$2.19