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Sequences Objectives: …to describe, extend, or find a missing element of a pattern Assessment Anchor: 7.D.1.1 – Recognize, reproduce, extend and/or describe patterns, sequences and relationships. Vocabulary alert!! SEQUENCE – a set of numbers that follow a pattern ARITHMETIC SEQUENCE – a sequence where each term is found by adding or subtracting the same number to the previous term GEOMETRIC SEQUENCE – a sequence where each term is found by multiplying or dividing the previous term by the same number NOTES Finding the pattern: 1. Consider a common difference (what’s being added or subtracted) 2. Consider a common ratio (what’s being multiplied or divided) 3. Consider an alternating pattern Write a rule for the sequence: TEMPLATE #1 (for arithmetic and geometric) “Start with ___, then _________________ repeatedly.” TEMPLATE #2 (for alternating patterns) “Start with ___, then alternate between _____________________.” Sequences EXAMPLES Sequence #1: 3, 7, 11, 15, 19, ___, ___, ___, … (common difference) +4 +4 RULE: +4 “Start with 3, then add 4 repeatedly.” Sequence #2: 4, 8, 16, 32, 64, ___, ___, ___, ___, … 4, 8, 16, 32, 64, 128, 256, 512, … Geometric sequence: (common ratio) RULE: +4 3, 7, 11, 15, 19, 23, 27, 31, … Arithmetic sequence: ×2 ×2 ×2 ×2 “Start with 4, then multiply by 2 repeatedly.” Sequence #3: 1.3, 2.9, 4.5, 6.1, ___, ___, ___, ___, … (common difference)? Arithmetic? or Geometric? 1.3, 2.9, 4.5, 6.1, ____, ____, ____, … (common ratio)? RULE: ___________________________________________________ Sequence #4: 48, 24, 12, 6, ___, ___, ___, … (common difference)? Arithmetic? or Geometric? 48, 24, 12, 6, ____, ____, ____, … (common ratio)? RULE: ___________________________________________________ “Don’t just THINK about what’s happening… find out, and write it down!” Sequences MORE EXAMPLES Sequence #5: 18, 10, 20, 12, 24, ___, ___, ___, … (difference)? Arithmetic? or Geometric? 18, 10, 20, 12, 24, ____, ____, ____, … (ratio)? RULE: ___________________________________________________________ Sequence #6: 3, 12, 13, 52, 53, ___, ___, ___, … (difference)? Arithmetic? or Geometric? 3, 12, 13, 52, 53, _____, _____, _____, … (ratio)? RULE: ___________________________________________________________ Sequence #7: 21.5, 21, 10.5, 10, 5, ___, ___, ___,… (difference)? Arithmetic? or Geometric? 21.5, 21, 10.5, 10, 5, ____, ____, ____, … (ratio)? RULE: ___________________________________________________________ Sequence #8: 18, 68, 34, 84, 50, ___, ___, ___, … (difference)? Arithmetic? or Geometric? 18, 68, 34, 84, 50, _____, _____, _____, … (ratio)? RULE: ___________________________________________________________