NUMBER PATTERNS.pptx

Revision of linear patterns.
Introduction to Quadratic number patterns

1. NUMBER PATTERNS GRADE 11

2. REVISION OF LINEAR NUMBER PATTERNS In Grade 10 we dealt with linear number patterns having a general term of the form . EXAMPLE Consider the following linear number pattern: 2 ; 7 ; 12 ; 17 ; …………. Determine the nth term and hence the 199th term. Which term of the number pattern is equal to 497?  

3. QUADRATIC NUMBER PATTERNS We will now focus on quadratic number patterns with general terms of the form:  

4. Introduction Consider, for example, the formula . We can generate the terms of the number sequence as follows: If we now consider the pattern 2; 5; 10; 17; 26; ………, we can investigate some interesting properties of this quadratic number pattern.  

5. Introduction Number patterns with a constant second differences are called quadratic number patterns . It is clear that this number pattern does not have a constant first difference as with linear number patterns. However… it does have a constant second difference .

6. The term of Quadratic Sequence   The question now arises as to how we would determine the general term of any given quadratic number pattern. Suppose that the general term of a particular quadratic number pattern is given by: The terms of the number pattern would then be:  

7. The term of Quadratic Sequence   You will notice that the constant second difference is given by the expression 2a The first term in the first difference row is given by   … and the first term is given by  

8. The term of Quadratic Sequence  

9. The term of Quadratic Sequence  

10. Example 1

11. Example 2