10. a. Write the first 4 terms of the sequence defined by an = (-1)n n!/3n; n20 C. b. For Fibonacci sequence (Fn), write the first 7 terms of the sequence if the recurrence relation is given by Fn = Fn-1 + Fn-2; Fo = 1, F₁= 1 If the golden ratio ~ 1.618, n ≥ 4, What is the next integer after 144 in Fn-1 the Fibonacci sequence?

Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: Consider the sequence given by bn = [1 + (-1)"] for ne N. 00 (a) List the first seven terms of this…

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Q: The term a, of the sequence defined by the recurrence relation and initial conditions a, = a,-1+4.a,…

A: The solution is given as

Q: Suppose that the sequence {a}, is =1 1,3, 5, 7,9, 11, 13, .. Find the sum s=E k=1

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Q: 10. Find a, for the sequence with generating function 2. (1-2) 1-1-2" - Hint You should "multiply"…

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Q: If F, = 6 and F2 = 3, list the first 8 terms of this Fibonacci-type sequence.

A: topic - fibonacci type sequence in fibonacci sequence, The next number is found by adding up the two…

Q: ow that an = 3· an-1+2. %3| 10 d En=o(an – an-1). (You don't have to compute 310 or 3º, ..., leave…

A: In this question, the concept of the sequence is applied. Sequence A series is created by a…

Q: Find a recurrence relation and initial conditions for the sequence 1, 4, 13, 40, 121, 364, ...

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Q: 2. The Fibonacci sequence (fn) := 0, 1, 1, 2, 3, 5, 8, . is an example of a recursive sequence with…

A: a)

Q: 16.Consider the first 3 terms of the sequence a, (where k 2 2). A. Give the first 3 terms of the…

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Q: 12. Show that the sequence {a} is a solution of the recurrence relation an = -3an-1 + 4an-2 if a) an…

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Q: Suppose that ho, hị, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D hy =…

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Q: Consider the sequence {ax}, defined by а, 3D 1, ад — 1, and ak 3 а-1+ ak-2 for k > 3. Compute as.

A: We have given two terms of sequence {a_k}, a_1=1 and a_2=1 and then sequence {a_k} is defined by…

Q: B1. Is the sequence (a,} where a, =-n+3 a solution of the recurrence relation a, -1+2a,-2+2n-9. B2.…

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Q: 3. Use iteration to guess an explicit formula for the sequence that satisfies the recurrence…

A: We have to find the nth term of the sequence .

Q: Suppose that g1, 92,93, ... is a sequence defined as follows: 91 = 3, 92 = 5, gk = 3gk-1 - 2gk-2 for…

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Q: 12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2,…

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Q: 3. Is the sequence defined by a = 2(-4)" + 3 a n solution of the recurrence relation a = -3 a +4a n…

A: Given Data:  To check the sequence 2-4n+3 is a solution of recurrence relation an=-3an-1+4an-2.

Q: 1. Write out the next 4 terms of the sequence a = a,' +n-1; a, =1 (this means %3D а, а,, а,, а,).

A: Given a0=1 and an+1=an3+n-1a1 means n=0So, a1=a0+1=13+0-1          =0a2=a1+1=03+1+-1              =0

Q: The sequence {a} begins with 2, 1,-1, -2, -1, 1, 2, ... n From the list below select a recurrence…

A: Option (B) is wrong as the initial conditions a0 = 3 and a1 = -1 are not true.    Option (C) is…

Q: Devise a recursive algorithm to find the nth term of the sequence defined by a = 1, a₁ = 2, and a =…

A: We can use a recursive algorithm to find the    n-th term of the sequence defined bya0 = 1, a1 = 2,…

Q: 8. Given the recursive sequence an = 3 · an-1 – 2 · an-2, where ao = 0, a1 = 1, (a) Find a2, a3, a4,…

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Q: 12. Find the first 5 terms of the sequence: 2n a, = (-1)" а) 2 n² +1 b) a, = 4a - 5 n-1 and ª1 =1

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Q: 6. Consider the sequence defined by the recursive formula an = 10 - a,-1 with ao = 2 (a) What are…

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Q: Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

A: If we take the sequence as {Un}, and if we can able to show that for all n=1,2,3, ...  Un+1>Un…

Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

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Q: Assume that a person invests $2000 each year in a tax-sheltered annuity at 10% interest compounded…

A: Given that,  a person invests $2000 each year in a tax-sheltered annuity at 10% interest compounded…

Q: 7. Give a recursive definition of the following: (a) the set of positive integers congruent to 3…

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Q: Q1. Let an = (-1)"an-1+ 2an-2, ao = 1 and a1 = 2. Determine the following terms of the sequence…

A: (i) The recurrence relation is given as follows: an=-1nan-1+2an-2                ...1

Q: 4. (20 points} Show that the sequence {an}, where an = 2(-4)"+3 is a solution of the recurrence…

A: In the given question we have to show that the sequence {an}, where an=2(-4)n+3 is the solution of…

Q: (b) Define another recursive sequence (hn) by removing fi, f3, f5,... from the bonacci sequence.…

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Q: Find a closed form for the infinite arithmetic sequence given by the recurrence system:  x1 = -1,…

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