Hint for Section 8.3 Question 3

3. Consider the second-order linear homogeneous recurrence relation r_k = r_k-1 + 2 r_k-2.
a) To find the two sequences which satisfy this relation you need to solve the characteristic equation of the relation t² - t - 2 = 0.

b) Now let  a_n = 3 b_n -  c_n  for all n0.  To show that for all integers k2, the sequence a_k also satisfies the recurrence relation r_k = r_k-1 + 2 r_k-2, you need to show that a_k = a_k-1 + 2 a_k-2. 

Back to Section 8.3
Full solution