Question

Let {an)."-o be a sequence defined by ao = 1, a1 = 4 and An = –2an–1 + 15an–2 for n > 2 There is a solution is of the form: an = aj(ri)" + az(ra)" for suitable constants Q1, Q2,11,r2 with ri < r2. Find these constants. ri = r2 = du = A2 =

Answer 1

The student's question involves finding constants for a sequence defined by a recurrence relation. We use the characteristic equation derived from the recurrence to find r1 and r2, then solve for a1 and a2 with the initial sequence conditions.

Step-by-step explanation:

The student is asking about finding the constants for a sequence that is defined by a recurrence relation. We are given a0 = 1, a1 = 4, and an = -2an-1 + 15an-2 for n > 1. The solution to this recurrence is assumed to be of the form an = a1(r1)n + a2(r2)n, where a1, a2, r1, and r2 are constants to be determined.

To find these constants, we would typically create a characteristic equation from the recurrence relation, which will be a quadratic equation whose roots will be r1 and r2. We find the roots of the characteristic equation and use the initial conditions of the sequence to solve for a1 and a2.