Computational Mathmatics

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ITSU2011 – Computational Mathematics Page 1 of 3

ITSU2011

Computational Mathematics

Activity 03

Victorian Institute of Technology Pty Ltd

ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E

ITSU2011 – Computational Mathematics Page 2 of 3

Q1) Calculate 𝑓(7) for the recursive sequence 𝑓(𝑥) = 2 ⋅ 𝑓(𝑥 − 2) + 3 which has a seed value

of 𝑓(3) = 11.

Answer: 53

Q2) Calculate 𝑓(8) for the recursive sequence 𝑓(𝑥) = 4 ⋅ 𝑓(𝑥 − 3) + 1 which has a seed value

of 𝑓(2) = 9.

Answer: 149

Q3) This question is one of the most famous recursive sequences and it is called the Fibonacci

sequence. It also demonstrates how recursive sequences can sometimes have multiple 𝑓(𝑥)'s in

their own definition.

It is defined below.

𝑓(𝑥) = 𝑓(𝑥 − 1) + 𝑓(𝑥 − 2)

Calculate 𝑓(3) with seed values of f(0) = 0 and 𝑓(1) = 1.

Answer: 2

Q4) Give a recursive definition of the sequence {𝑎𝑛 }, 𝑛 = 1, 2, 3, . . ., if

a) 𝑎𝑛= 7𝑛

b) 𝑎𝑛= 7𝑛

c) 𝑎𝑛= 7

Q6) Given the sequence: 25, 21, 17, 13, . ..

Write the explicit equation that models the sequence.

Q7) Write the explicit formula for the sequence −4, −6, −8, −10, . ..

Q8) What is the explicit rule for the sequence: 11, 22, 44, 88 …

Q9) There are 4,000 students attending a local community college and the number of students is

increasing by 5% each year. How many students will attend the college in 4 years?

Q10) Prove that √5 is irrational.

Victorian Institute of Technology Pty Ltd

ABN: 41 085 128 525 RTO No: 20829 TEQSA ID: PRV14007 CRICOS Provider Code: 02044E

ITSU2011 – Computational Mathematics Page 3 of 3

Q11) Prove that there is no greatest even integer.

Q12) Prove by contradiction that for any positive 𝑥 ∈ 𝑅, where 𝑅 is the positive number set.

𝑥 + 1

𝑥 ≥ 2, 𝑥 ≠ 0.