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SOL 6.17 Essential Questions: Types of numerical patterns What is the difference between an arithmetic and a geometric sequence? While both are numerical patterns, arithmetic sequences are additive and geometric sequences are multiplicative Complete the next three terms. State whether the pattern is geometric, arithmetic, or neither. Arithmetic Sequence (Common Difference) 1. 5, 7, 9, 11, 13, … 2. 1, 2, 4, 7, 11, 16, … 3. 80, 20, 5, 1.25, … 4. 27, 9, 3, 1, 1/3, … Geometric Sequence (Common Ratio) Strategies to Determine Patterns ***Directions: Fold in half vertically and cut on the dash line only*** Copy 1 sided to 2 sided EX: 3, 6, 9, 12 … common difference is 3 3, 9, 27, 81 … no common difference Linear and Exponential Growth Perfect Squares Triangular and other Polygonal Numbers Fibonacci Numbers Arithmetic Sequences Geometric Sequences A set of numbers arranged so that the difference between any two consecutive numbers is the same Common Difference The difference between the consecutive Numbers EX: 1, 3, 9, 27, 81 … common ratio is 3 8, 4, 2, 1, ½, ¼ … common ratio is ½ A set of numbers arranged so that the ratio between any two consecutive sequence elements is constant Common Ratio The number each tem is multiplied by to get the next term Examine the difference between each term, is it common? Arithmetic Examine the ratio between each term, is it common? Geometric