13. Is the sequence {a} a solution of the recurrence relationan = 8an-1-16a₁-2ifa) a₁ = 0?c) a₁ = 2¹?e) an =g) a₁ = (-4)"?= n4"?b) an= 1?d) a = 4"?=f) an 2.4" + 3n4"?a = n²4¹?h)

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Answered: 13. Is the sequence {a} a solution of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please explain.
. Which of the following are recurrence relations and which are not? (a) an = 2an-1 + 3an-2 (b) ak = 2(3)+5(4k) (c) bn-1= 2n² + 3n+4 (d) bk-1 = 2(bk-3)* = 2n² + Cn (f) Ck+1=3(5k+2) + 2(6+¹) +k² (g) dn 4dn+1 (h) 22+ 3+2= dk +dk+1 (e) Cn+1 = =
4. Consider the recurrence relation az = az-1 + 2k, k 2 1 and a, = 3. a) Write the first 5 terms of this sequence. b) Guess an explicit formula for this sequence. c) Check your formula solves the recurrence relation.
Identify the solution of the recurrence relation an=6an-1-12an-2+8an-3 with ap=-5, a1 = 4, and a2 = 88. Multiple Choice -5-20-n-20-1-13m².20-1 5-20+n-20+1+1372 20-1 -5-20+n-20-1-13n²-27-1 -5-20 n-20-1+13n2-27-1 D
(a) Is the sequence {(-2)"} is a solution of the recurrence relation a, = -an-1 + 2a,-2? Show your work. (b) Is the sequence {n®2"} a solution of the recurrence relation a, = 2a,-1 – 4a,-2? Show your work. (c) Is the sequence {2(-4)" + 3} is a solution of the recurrence relation a, Aan-2?Show your work. -3an-1 +
Solve the recurrence relation an 10an-1, a0 = 3. Choose the most appropriate option. O r= 10, a = 3 and a, = 3.10" O r= 10, a =3 and an = 10.3" O r= 11, a = 3 and an = = 11.3" O r= 10, a =4 and an = 10.4"
7. Solve the recurrence relation an 4an-2 for n > 2, given that ao 3 and a1 = -2.
Find the solution to the recurrence relation and initial condition. anan-1 + 2n +3, ao = 4 b) an = 2an-1 - 1, a0 = 1
4. (20 points) Show that the sequence {an}, where an = 2(-4)"+3 is a solution of the recurrence relation an + 3an-1 = 4an–2.
Please show the work necessary to get the answer.
Use the approach in Gauss problem to find the sum of 8+17+26+35+...+890
Solve the recurrence relation an = 7an-1 -12an-2 for all integers n ≥ 2, a = 1 and a₁ = 6.

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13. Is the sequence {a} a solution of the recurrence relation an = 8an-1-16a₁-2 if a) a₁ = 0? c) a₁ = 2¹? e) an = g) a₁ = (-4)"? = n4"? b) an = 1? d) a = 4"? = f) an 2.4" + 3n4"? a = n²4¹? h)