Computational Mathmatics

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 1 of 2

ITSU2011

Computational Mathematics

Activity 08

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 2

Part A)

1) Find gcd of the following pairs of numbers using Euclidean algorithm.

i. 15,5 ii. 26,8 iii. 1002,56 iv. -812,124

Part B)

1) Jazmin is completing an art project. She has two pieces of construction paper. The first piece is 44 centimetres wide, and the second piece is 33 centimetres wide. Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible. How wide should Jazmin cut each strip?

2) Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical packages. What is the greatest number of packages Tim can make?

3) Ronal and Tim both did their laundry today. Ronald does laundry every 6 days and Tim does laundry every 9 days. How many days will it be until Ronald and Tim both do laundry on the same day again?

4) Peter’s Party Zone sells cups in packages of 6 and plates in packages of 8. Shaniya is hosting a birthday party for her little sister and wants to have the same number of each item. What is the least number of packages of plates Shaniya needs to buy?

Part C)

1) Show that Latex formula forms an arithmetic progression.

2) Find 𝑇39 of 3, 10, 17, ….

3) What is the sum of the first 80 terms of the sequence −4,−1,2,5,…?

4) Show that the sequence 1, 3, 9 is a geometric progression.

5) Find the 6th of the following geometric sequence; 4, -2/3, 1/9, …

6) Find the sum to 12 terms of the geometric sequence 4, -6, 9, …

7) Does the limiting sum of the geometric series 27 + 9 + 3 + … exist? If so, find its value.

8) Express 0.973̅̅̅̅ as a fraction, using geometric series.