CHAPTER 4 Summary Patterns and sequences
• Numeric patterns are patterns that consist of numbers. Numeric patterns are also called number patterns.
• Geometric patterns are patterns that consist of shapes. • Another name for an ordered pattern of numbers is a sequence. • A recursive pattern is one in which any term in the pattern (usually from the 2nd or 3rd terms onwards) can be described in terms of the previous term (or terms).
• The Fibonacci sequence is a famous example of a recursive sequence. In the Fibonacci sequence, the first two terms (0 and 1) are given. The rest of the sequence grows from these two terms.
• We always need more than three terms to be able to fully describe a particular pattern.
The general rule
• If we can find the general rule that governs a pattern, we can apply this rule to find the general term of the pattern. We call this general term the nth term of the pattern, where n is the term’s position in the pattern.
• We use the notation Tn to mean the nth term of a pattern. So, T1 is the first term, T2 is the second term, and so on.
• We say that n is the independent variable and Tn is the dependent variable, because the value of Tn depends of the value of n.
• Once we have found the general rule for a pattern, we can write this rule in words, or in algebraic language.
• When there is a constant difference between successive terms in a number
pattern, the general term will be of the form Tn = an + c, where a is the common difference and c is a constant.
Representing patterns and relationships • We can represent number patterns in tables, flow diagrams, formulae and equations.
• Equivalent descriptions of the same rule are descriptions that look different, but that have the same meaning.
Chapter 4: Summary
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