Solved: Find the solution to each of these recurrence

QUESTION:

Find the solution to each of these recurrence relations and initial conditions. Use an iterative approach such as that used in Example 10.

Find the solution to each of these recurrence relations and initial conditions. Use an iterative approach such as that used in Example 10.

a) \(a_{n}=3 a_{n-1}, a_{0}=2\)

b) \(a_{n}=a_{n-1}+2, a_{0}=3\)

c) \(a_{n}=a_{n-1}+n, a_{0}=1\)

d) \(a_{n}=a_{n-1}+2 n+3, a_{0}=4\)

e) \(a_{n}=2 a_{n-1}-1, a_{0}=1\)

f) \(a_{n}=3 a_{n-1}+1, a_{0}=1\)

g) \(a_{n}=n a_{n-1}, a_{0}=5\)

h) \(a_{n}=2 n a_{n-1}, a_{0}=1\)

Equation Transcription:

Text Transcription:

a_n = 3a_n-1, a_0=2        

a_n =a_n-1 + 2, a_0=3  

a_n =a_n-1 + n, a_0=1          

a_n =a_n-1 + 2n + 3, a_0=4  

a_n = 2a_n-1 - 1, a_0=1                  

a_n = 3a_n-1 + 1, a_0=1  

a_n = na_n-1, a_0=5                  

a_n = 2na_n-1, a_0=1