1. Calculate the 12th term of the following sequence.3, -12, 48...2. For the following number patterns, write the recurrence relation:a) 5, 8.2, 11.4,14.6, ...maksb) 400, 50, 6.25, 0.781, ...marks)

According to guidelines we solve only first question

Answered: 1. Calculate the 12th term of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.
4. The following questions involve recurrence relations a. Write a recurrence relation for the following scenario: A person saving for retirement makes an initial deposit of $1,000 to a bank account earning interest at a rate of 3% per year compounded monthly. Each month she adds an additional $200 to the account. b. How much money will be in the account after 6 months? Round your answer to the nearest cent.
6.
2.21 Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how many ways can a person arrange to go on a sightseeing tour planned by this convention?
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3. A loan of $5,000 is charged a 1% monthly interest rate. An $80 payment is made each month. O Write a recurrence relation for the loan balance remaining at the beginning of month. Indicate which kind of recurrence relation describes the loan sequence (linear/not-linear, first/second/n-th order, homogeneous or not, constant/no-constant coefficients, divide-and-conquer) Solve the recurrence relation. Consider the geometric progression for the summation with r # 1: a + ar + a² + + ar-1 a ar 1 - 1 How much is left of the loan balance at the beginning of the 19th month?
Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries. i. How many different sequences are possible? ii. How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively? iii. How many different schedules begin and end with a knee surgery?
a. In the following, give the first five terms (b₁,b₂, b, b, b,), and identify the given recurrence relation (linear of degree k, nonlinear, homogeneous, etc.). (3 pts.) b₁ = 3b-1+4, for n≥2, and b₁ = 2 b. Solve the above recurrence relation using back tracking. (4 pts.)
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1. The Fibonacci sequence is given by the recurrence relation a, = a,-1+ a,-2; ao = 0, a =1. Write down the first 6 terms of the Fibonacci sequence. n-2:

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1. Calculate the 12th term of the following sequence. 3, -12, 48... 2. For the following number patterns, write the recurrence relation: a) 5, 8.2, 11.4,14.6, ...maks b) 400, 50, 6.25, 0.781, ... narks