Kenneth Rosen Edition 7 Exercise 2.4 Question 9 (Page No. 168)

Question

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

• A. $a_{n} = 6a_{n−1}, a_{0} = 2$
• B. $a_{n} = a_{n−1}^{2}, a_{1} = 2$
• C. $a_{n} = a_{n−1} + 3a_{n−2}, a_{0} = 1, a_{1} = 2$
• D. $a_{n} = na_{n−1} + n^{2}a_{n−2}, a_{0} = 1, a_{1} = 1$
• E. $a_{n} = a_{n−1} + a_{n−3}, a_{0} = 1, a_{1} = 2, a_{2} = 0$

Answer 1

a0= 2

a1 = 12

a2= 48

a3 = 288

a4= 1728