Thursday, August 11, 2016
Introduction
A sequence, in mathematics, is a string of objects, like numbers, that follow a particular pattern. The individual elements in a sequence are called terms. Some of the simplest sequences can be found in multiplication tables:
- 3, 6, 9, 12, 15, 18, 21, …
Pattern: “add 3 to the previous number to get the next number” - 0, 12, 24, 36, 48, 60, 72, …
Pattern: “add 12 to the previous number to get the next number”
Of course we can come up with much more complicated sequences:
- 10,–2 8,×2 16,–2 14,×2 28,–2 26,×2 52, …
Pattern: “alternatingly subtract 2 and multiply by 2 to get the next number” - 0,+2 2,+4 6,+6 12,+8 20,+10 30,+12 42, …
Pattern: “add increasing even numbers to get the next number”
Add the next three terms to each number pattern and explain how you calculated these terms:
1.1 2; 7; 12; 17; …
1.2 10; 8; 6; 4; …
1.3 ;... 2 `1 ; 3 4 3 ; ;2 2 4 1 1
1.4 1; 3; 9; 27; …
1.5 1; 1; 2; 3; 5; 8; 13; …
1.2 10; 8; 6; 4; …
1.3 ;... 2 `1 ; 3 4 3 ; ;2 2 4 1 1
1.4 1; 3; 9; 27; …
1.5 1; 1; 2; 3; 5; 8; 13; …
Video Lessons
Equations
Solving Equations
Linear equations can either have a single solution, infinite solutions, or no solutions. Learn how to determine the number of solutions to a given equation, and how to create equations with a desired number of solutions.
Learn how to solve linear equations that have the variable on both sides of the equation. For example, solve 2x+5=6x-3.
Learn how to solve linear equations with parentheses using the distributive property. For example, solve -9 - (9x - 6) = 3(4x + 6).
Do the following activity.
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