a. Let a1, a2,a3....b1,b2,b3...All satisfy the recurrence relation that the kth term equals 3times the (k-1)at term for all integers k≥1: ak= 3ak-1,bk=3bk-1,ck=3ck-1. But suppose the initial condition was a1=1, b1=0 and c1=2. Find:- A4, a6 ,a7 b2, b4, b5
a. Let a1, a2,a3....b1,b2,b3...All satisfy the recurrence relation that the kth term equals 3times the (k-1)at term for all integers k≥1: ak= 3ak-1,bk=3bk-1,ck=3ck-1. But suppose the initial condition was a1=1, b1=0 and c1=2. Find:- A4, a6 ,a7 b2, b4, b5
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 57EQ
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a. Let a1, a2,a3....b1,b2,b3...All satisfy the recurrence relation that the kth term equals 3times the (k-1)at term for all integers k≥1:
ak= 3ak-1,bk=3bk-1,ck=3ck-1. But suppose the initial condition was a1=1, b1=0 and c1=2.
Find:-
- A4, a6 ,a7
- b2, b4, b5
b. Show that the sequence 1,-1!, 2!, -3!,......(-1)nn!.…for n≥0, satisfies the recurrence relation sk=-K.sk-1 for all integers K≥1.
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