Find the first five terms of the sequence defined by each

QUESTION:

Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions.

a) \(a_{n}=6 a_{n-1}, a_{0}=2\)

b) \(a_{n}=a_{n-1}^{2}, a_{1}=2\)

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

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

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

Equation Transcription:

Text Transcription:

a_n = 6a_n-1, a_0 = 2

a_n = a_n-1^2, a_1 = 2

a_n = a_n-1 + 3a_n-2, a_0 = 1, a_1 = 2

a_n = na_n-1 + n^2a_n-2, a_0 = 1, a_1 = 1

a_n = a_n-1 + a_n-3, a_0 = 1, a_1 = 2, a_2 = 0