QUESTION 6a)Find the recurrence formula the sequence 2,4,6,8,...b)Find the first 6 terms of the sequence defined by the recurrence relationan=an-1+an-3, if n23with the initial conditions ao=1, a1=2, a2=1.

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Answered: QUESTION 6 a) Find the recurrence…

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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6. Let a be the number of 1 x n tile designs you can make using 1 × 1 squares available in 4 colors and 1 x 2 dominoes available in 5 colors. a. First, find a recurrence relation to describe the problem. Explain why the recurrence relation is correct (in the context of the problem). b. Write out the first 6 terms of the sequence a1, a2,.... c. Solve the recurrence relation. That is, find a closed formula for an.
Question 1 A sequence is defined recursively as follows. an+1 = 2¹+ an-1 where n ≥ 1. Part a) Reindex the recursively defined sequence by substituting n - 1 for n. Part b) Then verify that the first value of n in the reindexed relation also gives a₂ = 2 + ao and consequently the given recurrence relation and the given recurrence relation both produce the same sequence.
Find the first 5 terms of the sequence from the recurrence relation, given: • a, = 4 • a, = 5 • an = an-1 + 5а,р-2 a {4, 5, 25, 50, 176} b {4, 5, 25, 50, 175) {4, 5, 26, 50, 175} {4, 5, 25, 51, 175} O OOO
QUESTION 6 a) Find the recurrence formula the sequence 2,4,6,8,.. b) Find the first 6 terms of the sequence defined by the recurrence relation an=an-1+an-3, if n23 with the initial conditions a0=D1, a1=2, a2=1.
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Consider the recurrence relation an = Зап - 1 + 4аm -2 with initial terms ao 4 and a1 5. a. Find the next two terms of the sequence (a2 and a3 ). a2 = a3 b. Solve the recurrence relation. That is, find a closed formula for the nth term of the sequence. An
4. Consider this recurrence relations an an-1 + 2an-2. (a) What sequence do you get if the initial conditions are ao=3, a₁=7? Give a closed formula for this sequence. (b) What sequence do you get if the initial conditions are ao=2, a₁=7? Give a closed formula. (c) What if ao 2 and a₁=5? Find a closed formula.

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QUESTION 6 a) Find the recurrence formula the sequence 2,4,6,8,... b) Find the first 6 terms of the sequence defined by the recurrence relation an=an-1+an-3, if n23 with the initial conditions ao=1, a1=2, a2=1.