Answered: The closed form solution to the…

The closed form solution to the recurrence relation a(n)= a(n-1) + 4 with a(0) = 3 is (A) a(n+1)= a(n) - 3 (B) a(n) = 4 + 3n (C) a(n) = 3 + 4n (D) a(n) = 4n-3 (E) None of the above

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Consider the following second-order recurrence relation and its characteristic polynomial A(x): a, =…

Q: 9. Given a recurrence relation a₁ = 8an-1- 16an-2, with a = 2 and a₁ = 6 Find explicit formula for…

A: The solution is given as

Q: What is the characteristic polynomial for the recurrence relation an = 4an-1 + 8? (1) (x+4)(x - 1)…

Q: Find the general solution of the recurrence relation: a) an = 7an-1-12an -2 + 2n(5¹) b) Show that…

A: a) Arrange as The auxiliary equation is Multiplying by gives , so (m-3)(m-4) = 0, so m=3 or m=4So…

Q: What is the general form of the particular solution of the linear nonhomogeneous recurrence relation…

A: Given nonhomogeneous equation isan=−6an−1−8an−2+F(n)Then the corresponding homogeneous equation…

Q: Select the correct general solution for the recurrence relation given below: fn = 10 · fn-1 – 25 ·…

Q: Using P3(x) =[5x³ – 3x] and P,(x) =[35x* – 30x² +3] %3D

A: It is known that the Legendre polynomial satisfies the recurrence relation,…

Q: Which of the following recurrence relations is nonlinear ? (1) an - 3an-1 - 5an-2 = 0 (2) an -…

Q: Prove that if the recurrence relation Xn = axn-1 + bxn-2 has values , λ1 ≠λ2, then the solution will…

Q: (a) Let (F(n))n>0 be a sequence of real numbers and let k e N. Explain what it means for (F(n))n>o…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Solve the following recurrence relations: (i) an = an-1 + 2an-2 (ii) where the initial conditions…

A: Given: Recurrence relations: an=an-1+2an-2; a0=0, a1=1an+2-5an+1+6an=2; a0=1, a1=-1We…

Q: Q10. In this problem we will solve a recurrence using generating function an = 5an-1-6 an-2, ao=1,…

Q: or, Recurrence Formulae : ¨ (2n + 1) xP₂ = (n + 1) Pn+j+nP,-1 (n+1) Pn+1 = (2n + 1) xP₁ − nP,. -

A: ⁰0⁰

Q: Find the solution to the recurrence relation an = -2. ao = un - 2 and a1 = −2an-1+8an-2 with initial…

A: Given recurrence relation an=-2an-1+8an-2

Q: 1 1 + (1 – x)3 4 fg(x) (1 — Зx) | Find a recurrence relation for an. Note g(x) = >, an*x" %3D

Q: What is the form of the particular solution of the linear non-homogeneous recurrence relation an =…

Q: Find x, y, z, and w. x y z 8 (x + 7)] = [ (2² (2x - 3) X -1 W (9 + y) -8

Q: 10. Show that an = : 2n5n is also a solution to the recurrence relation an = 7an-1-10an-2. What…

Q: An= -An-1+12An-2 A0=5 A1=8 A2=52 A3=44 Using the Generating function method, show the…

Q: A model for the number Ln of lobsters caught per year is based on the assumption that the number of…

Q: Use Eq. (1) to prove the recurrence relation: (n + 1) Pr+1 = x(2n + 1) P – n Pn-1

Q: What is the characteristic polynomial for the recurrence relation an = 5an-1 –7.2 (1) (x + 5)(x – 1)…

A: Given recurrence relation an=5an-1-7

Q: What is the degree of the recurrence relation an+1 -4an+3-an-1=0 ? (1) 1 (2) 4 (3) 3 (4) 2 A) Choice…

Q: . Solve the following recurrence relations: (1) аn+1 — а, %3D п* , п 20, аg — 1 | (ii) аn+2 — 2ал+1…

A: Solution for i: Given an+1-an=n2, n≥0, a0=1 Let the generating function is G(x)=∑n≥0anxn We can…

Q: Please help me with these questions. I dont understand what I did wrong. Kindly input correct…

Q: 12. What is the solution of the recurrence relation a, = 4a,n-1+ 5an-2 with ao = 2 and %3D a, = 4?…

Q: Consider the following second-order recurrence relation and its characteristic polynomial A(x): a, =…

A: Consider the provided question, According to you we have to solve only part (c). (c) (i)

Q: Use telescopic method to solve the recurrence relation f(0) = 4 and f(n) = f(n − 1) + 2n − 1 for all…

A: Given recurrence relation, fn=fn-1+2n-1. f0=4 We have to use telescopic method to solve this…

Q: (i) A pixie can climb stairs one, two or four steps at a time. Find a recurrence relation for an:…

A: For (i), We are given that a pixie can climb stairs one, two or four steps at a time. Now, we need…

Q: A car costs $130 to hire for the first day and $110 for each extra day. If C(k) is the cost of…

Q: What is the characteristic polynomial for the recurrence relation an = 7an-1+n · (-6)".? (1) (x +…

Q: Consider the recurrence relation an+2 = 5αn+1 − 6an+n² with ao = 0 and ₁ - (a) Find a closed form…

A: Given difference equationan+2=5an+1−6an+n2Corresponding homogeneous equation isan+2−5an+1+6an=0Let…

Q: this sequence? x0 = 0 x1= 0 x2 = 1 x3 = 1 x4 = 2 x5 = 4 x6 = 7

A: Topic:- algebra

Q: . Which of the following are recurrence relations and which are not? (a) an = 2an-1 + 3an-2 (b) ak =…

A: Please find attachment

Q: Please solve the recurrence relation (1) T(n) = T(3n/13) + T(5n/17) + n

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: For each recurrence relation below find the solution using the initial conditions given. (a) an =…

A: By Bartleby policy I have to solve only first one as these are all unrelated & lengthy…

Question

The closed form solution to the recurrence relation a(n) = a(n-1) + 4 with a(0) = 3 is
(A) a (n+1)= a(n) - 3 (B) a(n) = 4 + 3n
(C) a(n) = 3 + 4n
(D) a(n) = 4n-3
(E) None of the above.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

please help me fast so that I will give you good rating
Prove the following recurrence relation: xP(x) – P-1(x) = nPn(x).
Solve the recurrence relation, given: • ao = 3 • a₁ = 4 . • an = 5an-1-6an-2 Remember: • The theorem is an = c₁an-1 + c₂an-2. -b± √b² - 4ac 2a • The quadratic formula is O a O b Oc Od an = 5(4)" -2(3)" an = 5(2)"-2(3)" an = 5(2)"+2(3)" an = 5(3)" -2(3)"
What is the general solution for the recurrence relation tn = 13tn-1 – 36tn-2 ? (1) tn = c1(-4)" + c2(9)" (2) tn = c1(4)" + c2(9)" (3) tn = c1(-4)" + c2(-9)" (4) tn = c1(4)" + c2(-9)"
nan (a – 3)n-1 + x Σ an (x - 3)" = 0, - n=0 then the recurrence relation can be written as (n + 1)an+1 – an−1 + 3an = 0, (n + 1)an+1 + an−1 + an=0, – (n+1)an+1 + an−1 + 3an = 0, η>1 (n + 2)an+2 + an−1 + an = 0, (n + 2)an+2 + an−1 + an = 0, - Q6. 11 Σ n=1 = (a) αι = =do, (b) αι = 3a0 , (c) a1 = - –3ao, (d) a1 = do , (e) a1 = =do , n21 n>1 η21 η>1
What is the form of the particular solution of the linear non-homogeneous recurrence relation. [hint: the characteristic equation factorised is (x+5)²(x+1)²] an = -12an-1-36an-2 - 60an-3-25an-4+ (3n³ + 1) (-5)" - 1 −
2. (a) Let (F(n)n>o be a sequence of real numbers and let k E N. Explain what it means for (F(n))n>o to satisfy a (k + 1)-term recurrence relation with constant coefficients. (b) Suppose (F(n))n>0 satisfies the following recurrence relation: F(n) = aF(n – 1) for n>1 and F(0) = b, where a, b e N. Compute the values of F(1), F(2), and then find a general formula for F(n) for arbitrary n > 0. (c) If (F(n))n>0 is a sequence, write down the generating function for (F(n))n>0- (d) A sequence (F(n))n>0 has the following initial terms F(0) = 2, F(1) = 4, F(2) = 10 and satisfies the recurrence relation F(n) = 3F(n – 1) – 2 for n > 1. 1 (i) Show that this sequence also satisfies the relation F(n) = 4F(n – 1) – 3F(n – 2) for n> 2. (ii) Using the generating functions approach, find a closed form for F(n) for all n> 0.
Is there a way you can show the master method or master theorem being used ?