Introduction to Unit 1: Patterns & Sequences Mathematics 12 Foundations

Definitions : Sequence :   An arrangement of numbers, symbols, or pictures in order.   Each item or term follows another according to a rule. Example :   {a, b, c, d, e} is the sequence of the first 5 letters alphabetically  {0, 1, 0, 1, 0, 1,...}  {20, 25, 30, 35,...}

Definitions : Term :   Each item in a sequence Finite Sequence:   A sequence which eventually ends. Example : {1, 3, 5, 7} 4. 4.Infinite Sequence:   A sequence which continues endlessly. Example : {1, 2, 3, 4,...}

Definitions : 5. 5.Fibonacci Sequence:   A sequence which is determined by calculating the sum of the previous two terms.   Terms one and two have the value of 1.   Example : {1, 1, 2, 3, 5, 8, …} 6. 6.Fibonacci Number:   A term in the Fibonacci sequence.

Fibonacci Sequence:   0, 1, 1, 2, 3, 5, 8, 13, 21, 34,...   The next number is found by adding the two numbers before it together   The 2 is found by adding the two numbers before it (1+1)   The 21 is found by adding the two numbers before it (8+13)

Investigation #1 – Properties of Designs (page 2)   In most types of construction, it is important to make and extend patterns. A bricklayer builds towers using an odd number of bricks in each row.   Each new tower has one more row than the previous tower had.   Tiffany, a bricklayer, wants to know the number of bricks needed to build a tower with 10 rows.

Investigation #1 – Properties of Designs (page 2)   She writes the number of bricks for each tower as a term in a sequence : {1, 4, 9 …}.

Purpose   Describe a patterning rule for extending a sequence of numbers symbols, or pictures. Procedure   Use a geometrical pattern to draw below the next three towers in the bricklayer’s project above.

What is the Pattern or Sequence?   What numbers will we write below for this sequence ? {___, ___, ___, ___, ___, ___, ___, ___, ___, ___ …}

Draw a graph showing the number of bricks versus the number of rows in the tower.

Questions: 1. 1.Choose ONE of the following which best describes the shape of the graph you drew above.   Line   Parabola   Sine   Cosine   Absolute Value

2. 2.Explain using the idea of slope, why the graph you plotted can’t be a linear relationship Describe a rule for finding the number of bricks in a tower, if you know the number of rows in the tower.

4. 4.Use the rule from question #3 to determine the number of bricks in a tower with the following number of rows.

5. 5.Fill in the table below with the missing information..