1_2_patterns_sequences.ppt
- 2. Patterns and Sequences Patterns refer to usual types of procedures or rules that can be followed. Patterns are useful to predict what came before or what might come after a set a numbers that are arranged in a particular order. This arrangement of numbers is called a sequence. For example: 3,6,9,12 and 15 are numbers that form a pattern called a sequence The numbers that are in the sequence are called terms.
- 3. Patterns and Sequences Arithmetic sequence (arithmetic progression) – A sequence of numbers in which the difference between any two consecutive numbers or expressions is the same. Geometric sequence – A sequence of numbers in which each term is formed by multiplying the previous term by the same number or expression.
- 4. Arithmetic Sequence Find the next three numbers or terms in each pattern. ,... 22 , 17 , 12 , 7 a. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to add 5 to each term. 22,... 17, 12, 7, a. 5 5 5 ,... 22 , 17 , 12 , 7 a. The next three terms are: 27 5 22 32 5 27 37 5 32 37 , 32 , 27
- 5. Arithmetic Sequence Find the next three numbers or terms in each pattern. 36,... 39, 42, 45, b. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to add the integer (-3) to each term. 36,... 39, 42, 45, b. ) 3 ( ) 3 ( ) 3 ( The next three terms are: 33 ) 3 ( 36 30 ) 3 ( 33 27 ) 3 ( 30 36,... 39, 42, 45, b. 27 , 30 , 33
- 6. Geometric Sequence Find the next three numbers or terms in each pattern. 81,... 27, 9, 3, b. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to multiply 3 to each term. 81,... 27, 9, 3, b. 3 3 3 The next three terms are: 243 3 81 729 3 243 1 2187 3 729 2 36,... 39, 42, 45, b. 27 , 30 , 33
- 7. Geometric Sequence Find the next three numbers or terms in each pattern. 64... 128, 256, 528, b. Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to divide by 2 to each term. 64,... 128, 256, 528, b. 2 1 or 2 2 1 or 2 2 1 or 2 The next three terms are: 32 2 64 2 1 1 64 32 2 64 or 16 2 32 2 1 1 32 16 2 32 or 8 2 16 2 1 1 16 8 2 16 or 64,... 128, 256, 528, b. 8 , 16 , 32 Note: To divide by a number is the same as multiplying by its reciprocal. The pattern for a geometric sequence is represented as a multiplication pattern. For example: to divide by 2 is represented as the pattern multiply by ½.
- 8. Geometric Sequence Find the next three expressions or terms in each pattern. .. 16 , 8 , 4 , 2 b. m m m m Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to multiply by 2 to each term or expression. ,... 16 , 8 , 4 , 2 b. m m m m 2 2 2 The next three terms are: m m 32 2 16 m m 128 2 64 m m 64 2 32 ,... 16 , 8 , 4 , 2 b. m m m m m m m 128 , 64 , 32
- 9. Arithmetic Sequence Find the next three expressions or terms in each pattern. .. 11 8 , 8 6 , 5 4 , 2 2 b. m m m m Look for a pattern: usually a procedure or rule that uses the same number or expression each time to find the next term. The pattern is to add 2m+3 to each term or expression. ,... 11 8 , 8 6 , 5 4 , 2 2 b. m m m m 3 2 m 3 2 m 3 2 m The next three terms are: 15 10 3 2 11 8 m m m 21 14 3 2 18 12 m m m 18 12 3 2 15 10 m m m ,... 11 10 , 8 6 , 5 4 , 2 2 b. m m m m 21 14 , 18 12 , 15 10 m m m