Given the sequence defined with the recurrence relation:
Given the sequence defined with the recurrence relation:
$$ \begin{array}{l} a_{0}=2 \\ a_{k}=4 a_{k-1}+5 \text { for } n \geq 0 \end{array} $$
A. (3 marks) Terms of Sequence Calculate \(a_{1}, a_{2}, a_{3}\) Keep your intermediate answers as you will need them in the next questions
B. ( 7 marks) Iteration Using iteration, solve the recurrence relation when \(n \geq 0\) (i.e. find an analytic formula for \(a_{n}\) ). Simplify your answer as much as possible, showing your work. In particular, your final answer should not contain \(\sum\) and \(\prod\). You must show your work to get full marks.
Homework Answers
Request Answer!
We need at least 9 more requests to produce the answer.
1 / 10 have requested this problem solution
The more requests, the faster the answer.
Given the sequence an defined recursively as follows: an 3an-1+2 for n 2 1 Al Terms of a Sequence...
Given the sequence an defined recursively as follows: an 3an-1+2 for n 2 1 Al Terms of a Sequence (5 marks) Calculate ai , аг, аз, а4, а5 Keep your intermediate answers as you will need them in the next question. A2 Iteration (5 marks) Using iteration, solve the recurrence relation when n21 (i.e. find an analytic formula for an). Simplify your answer as much as possible, showing your work and quoting any formula or rule that you use. In...
The sequence { ak } is defined by the recurrence relation ak+2 = 3ak+1 + 4ak...
The sequence { ak } is defined by the recurrence relation ak+2 = 3ak+1 + 4ak with initial conditions do = 0, Q1 = 1. (a) Express the recurrence relation as a matrix difference equation Uk+1 = Auk (b) Find the general formula for ak. (Advise: You can check your answer by comput- ing the first few terms.)
: Let a1, a2, a3, . . . be the sequence of integers defined by a1 = 1 and defined for n ≥ 2 by the recurrence relation a...
: Let a1, a2, a3, . . . be the sequence of integers defined by a1 = 1 and defined for n ≥ 2 by the recurrence relation an = 3an−1 + 1. Using the Principle of Mathematical Induction, prove for all integers n ≥ 1 that an = (3 n − 1) /2 .
For each of the following problems write a recurrence relation describing the running time of eac...
For each of the following problems write a recurrence relation
describing the running time of each of the following algorithms and
determine the asymptotic complexity of the function defined by the
recurrence relation. Justify your solution using substitution and
carefully computing lower and upper bounds for the sums. Simplify
and express your answer as Θ(n k ) or Θ(n k (log n)) wherever
possible. If the algorithm takes exponential time, then just give
exponential lower bounds.
5. func5 (A,n) /*...
(12 points) For each sequence described below, first find a recurrence relation for that sequence...
Discrete Math for COMP:
(12 points) For each sequence described below, first find a recurrence relation for that sequence and then solve your recurrence relation. (a) The sequence Sn where 80 = 0, si-l and, for n 〉 1, sn s the average of the previous two terms of the sequence. (b) The sequence bn whose nth term is the number of n-bit strings that don't have two zeros in a rovw (c) The sequence en whose nth term is...
3. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution...
3. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution and upper and/or lower bounds, when necessary. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as O(n*) or O(nk log2 n) whenever possible. If the algorithm is exponential just give exponential lower bounds c) T(n) T(n-4) cn, T(0) c' d) T(n) 3T(n/3) c, T() c' e) T(n) T(n-1)T(n-4)clog2n, T(0) c'
3. Determine the...
A sequence is defined by the first-order recurrence relation: an=5an-1+3 a0=4 a) Write out the first...
A sequence is defined by the first-order recurrence relation: an=5an-1+3 a0=4 a) Write out the first 5 terms of this sequence. b) Given that: an=A*5n+B Show that A=19/4 and B=-3/4. c) Use mathematical induction to prove that ?n = 19/4 × 5n – 3/4
3. 0 marks Suppose you have an algorithm which has the following recurrence relation for W(n),...
3. 0 marks Suppose you have an algorithm which has the following recurrence relation for W(n), assuming n is a power of 2, i.e. assuming n-2, k20: for n for n- W()-2W(n/2)+2n+ 2 W(n)- Using back substitution and assuming n is a power of 2, ie. n-2, find an exact (ie non-recursive) formula for Win). Be sure to show your work and to simplify your final answer as much as possible. Note that you do NOT need to verify your...
MATLAB 1. The Fibonacci sequence is defined by the recurrence relation Fn = Fn-1+Fn-2 where Fo...
MATLAB
1. The Fibonacci sequence is defined by the recurrence relation Fn = Fn-1+Fn-2 where Fo = 0 and F1 = 1. Hence F2 = 1, F3 = 2, F4 = 3, etc. In this problem you will use three different methods to compute the n-th element of the sequence. Then, you will compare the time complexity of these methods. (a) Write a recursive function called fibRec with the following declaration line begin code function nElem = fibrec (n) end...
Write a recurrence relation describing the worst case running time of each of the following algorithms,...
Write a recurrence relation describing the worst case running time of each of the following algorithms, and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution by using substitution or a recursion tree. You may NOT use the Master Theorem. Simplify your answers, expressing them in a form such as O(nk) or (nklog n) whenever possible. If the algorithm takes exponential time, then just give an exponential lower bound using the 2 notation. function...
Given the sequence an defined recursively as follows: an 3an-1+2 for n 2 1 Al Terms of a Sequence (5 marks) Calculate ai , аг, аз, а4, а5 Keep your intermediate answers as you will need them in the next question. A2 Iteration (5 marks) Using iteration, solve the recurrence relation when n21 (i.e. find an analytic formula for an). Simplify your answer as much as possible, showing your work and quoting any formula or rule that you use. In...
The sequence { ak } is defined by the recurrence relation ak+2 = 3ak+1 + 4ak with initial conditions do = 0, Q1 = 1. (a) Express the recurrence relation as a matrix difference equation Uk+1 = Auk (b) Find the general formula for ak. (Advise: You can check your answer by comput- ing the first few terms.)
For each of the following problems write a recurrence relation
describing the running time of each of the following algorithms and
determine the asymptotic complexity of the function defined by the
recurrence relation. Justify your solution using substitution and
carefully computing lower and upper bounds for the sums. Simplify
and express your answer as Θ(n k ) or Θ(n k (log n)) wherever
possible. If the algorithm takes exponential time, then just give
exponential lower bounds.
5. func5 (A,n) /*...
Discrete Math for COMP:
(12 points) For each sequence described below, first find a recurrence relation for that sequence and then solve your recurrence relation. (a) The sequence Sn where 80 = 0, si-l and, for n 〉 1, sn s the average of the previous two terms of the sequence. (b) The sequence bn whose nth term is the number of n-bit strings that don't have two zeros in a rovw (c) The sequence en whose nth term is...
3. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution and upper and/or lower bounds, when necessary. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as O(n*) or O(nk log2 n) whenever possible. If the algorithm is exponential just give exponential lower bounds c) T(n) T(n-4) cn, T(0) c' d) T(n) 3T(n/3) c, T() c' e) T(n) T(n-1)T(n-4)clog2n, T(0) c'
3. Determine the...
3. 0 marks Suppose you have an algorithm which has the following recurrence relation for W(n), assuming n is a power of 2, i.e. assuming n-2, k20: for n for n- W()-2W(n/2)+2n+ 2 W(n)- Using back substitution and assuming n is a power of 2, ie. n-2, find an exact (ie non-recursive) formula for Win). Be sure to show your work and to simplify your final answer as much as possible. Note that you do NOT need to verify your...
MATLAB
1. The Fibonacci sequence is defined by the recurrence relation Fn = Fn-1+Fn-2 where Fo = 0 and F1 = 1. Hence F2 = 1, F3 = 2, F4 = 3, etc. In this problem you will use three different methods to compute the n-th element of the sequence. Then, you will compare the time complexity of these methods. (a) Write a recursive function called fibRec with the following declaration line begin code function nElem = fibrec (n) end...
Write a recurrence relation describing the worst case running time of each of the following algorithms, and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution by using substitution or a recursion tree. You may NOT use the Master Theorem. Simplify your answers, expressing them in a form such as O(nk) or (nklog n) whenever possible. If the algorithm takes exponential time, then just give an exponential lower bound using the 2 notation. function...
Most questions answered within 3 hours.
-
An short-seller in Tesla is worried the latest management
earnings forecast is too aggressive and the...
asked 36 minutes ago -
Question 3 (1 point)
Fill in the blank. Speed Car Rental company found that the tire...
asked 36 minutes ago -
1. A copper wire is 26.61 cm long and weighs 1.265 g. The
density of copper...
asked 13 minutes ago -
Remember that a concept sketch consists of a sketch (or
series of sketches), labels, and complete...
asked 16 minutes ago -
on a newly discovered planet, the period of a pendulum with a
length of 2 m...
asked 18 minutes ago -
Why [M(CN)6] is not organometallic even it has metal
to carbon bond too
asked 24 minutes ago -
mstar electric has a bond issue outstanding that has a 20 year
life, a $1,000 par...
asked 32 minutes ago -
This is a Business Writing Question:
Common Types of Faulty Sentence Logic:
A. Mixed constructions
B....
asked 32 minutes ago -
Skinner asserts that science, and the common view of science, has
been tarnished. Explain his evidence...
asked 35 minutes ago -
A grocery store's receipts show that Sunday customer purchases
have a skewed distribution with a mean...
asked 42 minutes ago -
A 0.035 mol sample of a weak acid, HA, is dissolved in 437 mL of
water...
asked 53 minutes ago -
a sample of Ar gas has a volume of 6.30 L with an unknown
pressure. the...
asked 54 minutes ago