Consider the recurrence relation an = 2an-1 + 3an-2 with first two terms a0 = 9 and a1 = 15. a. Write out the first 5 terms of the sequence defined by this recurrence relation. a2 = , a3 = , a4 = , ... b. Solve the recurrence relation. That is, find a closed formula for an. an =

          Consider the recurrence relation an = 2an-1 + 3an-2 with first two terms a0 = 9 and a1 = 15.
a. Write out the first 5 terms of the sequence defined by this recurrence relation.
a2 = , a3 = ,
a4 = , ...
b. Solve the recurrence relation. That is, find a closed formula for an.
an =

Consider the recurrence relation an = 2an-1 + 3an-2 with first two terms a0 = 9 and a1 = 15.
a. Write out the first 5 terms of the sequence defined by this recurrence relation.
a2 = , a3 = ,
a4 = , ...
b. Solve the recurrence relation. That is, find a closed formula for an.
an =

Added by Robert P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/07/2023

Step 1

To do this, we use the recurrence relation to find the next term, an-1: an-1 = 9 + 15 = 26. Show more…

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Consider the recurrence relation an = 2an-1 + 3an-2 with first two terms a0 = 9 and a1 = 15. a. Write out the first 5 terms of the sequence defined by this recurrence relation: a0 = 9 a1 = 15 a2 = 2a1 + 3a0 = 2(15) + 3(9) = 30 + 27 = 57 a3 = 2a2 + 3a1 = 2(57) + 3(15) = 114 + 45 = 159 a4 = 2a3 + 3a2 = 2(159) + 3(57) = 318 + 171 = 489 a5 = 2a4 + 3a3 = 2(489) + 3(159) = 978 + 477 = 1455 b. Solve the recurrence relation: That is, find a closed formula for an. To find a closed formula for an, we can use the characteristic equation method. The characteristic equation is r^2 - 2r - 3 = 0. Factoring the equation, we get (r - 3)(r + 1) = 0. So the roots of the characteristic equation are r = 3 and r = -1. Therefore, the closed formula for an is given by: an = A(3^n) + B(-1^n), where A and B are constants determined by the initial conditions a0 = 9 and a1 = 15.