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Iterative Patterns

Iterative Patterns. Arithmetic and Geometric. Define Iterative Patterns …. Iterative Patterns follow a specific RULE . Examples of Iterative Patterns: 2, 4, 6, 8, 10, … 2, 4, 8, 16, 32, … 96, 92, 88, 84, 80, … 625, 125, 25, 5, …. Rule: add 2 Rule: multiply by 2 Rule: subtract 4

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Iterative Patterns

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  1. Iterative Patterns Arithmetic and Geometric

  2. Define Iterative Patterns… • Iterative Patterns follow a specific RULE. • Examples of Iterative Patterns: • 2, 4, 6, 8, 10, … • 2, 4, 8, 16, 32, … • 96, 92, 88, 84, 80, … • 625, 125, 25, 5, … Rule: add 2 Rule: multiply by 2 Rule: subtract 4 Rule: multiply by 1/5

  3. Arithmetic Sequence • Is an Iterative Pattern where the rule is to ADD or SUBTRACT to get the next term. • We call the number that you ADD or SUBTRACT the COMMON DIFFERENCE. • Examples of Arithmetic Sequences: • 3, 6, 9, 12, 15… • 85, 90, 95, 100, 105, … • 5, 3, 1, -1, -3, -5, … d = 3 d = 5 d = -2

  4. Determine if the sequence is Arithmetic. If so, find the common difference. Yes. d = 2 No Yes, d = 1/92/9, 3/9, 4/9, 5/9, 6/9, … Yes. d =-7 No Yes. d = -3 • 4, 6, 8, 10, 12, … • 14, 12, 11, 9, 8, … • 2/9, 1/3, 4/9, 5/9, 2/3, … • 99, 92, 85, 78, 71, … • ½, ¼, 1/8, 1/16, 1/32, … • 9, 6, 3, 0, -3, …

  5. Write the first 5 terms of the Arithmetic Sequence. • a1 = 2, d = 1 • a1 = 2 means that the first term in your sequence is 2. • d = 1 means the common difference is 1. • Since “1” is positive, you will add “1” each time to get to the next term in the sequence. • The first 5 terms of the sequence are: • 2, 3, 4, 5, 6

  6. Write the first 5 terms of the Arithmetic Sequence. • a1 = 3, d = 7 • a1 = 0, d = 0.25 • a1 = 100, d = -5 • a3 = 6, d = -4 3, 10, 17, 24, 31 0, 0.25, 0.5, 0.75, 1 100, 95, 90, 85, 80 14, 10, 6, 2, -2

  7. Geometric Sequences • Is an Iterative Pattern where the rule is to MULTIPLY to get the next term. • We call the number that you multiply the COMMON RATIO. • Examples of Geometric Sequences: • 4, 8, 16, 32, 64, 128, … • 1000, 100, 10, 1, 0.1, … • 81, 27, 9, 3, … Rule: r = 2 Rule: r = 1/10 Rule: r = 1/3

  8. Determine if the sequence is Geometric.If so, find the common ratio. No Yes. r = 3 Yes. r = -1 Yes. r = 1.5 Yes. r = 23/16, 6/16, 12/16, 24/16 Yes. r = 2 • -4, -2, 0, 2, 4, … • 2, 6, 18, 54, 162, … • 2/3, -2/3, 2/3, -2/3, 2/3, … • 1, 1.5, 2.25, 3.375, … • 3/16, 3/8, ¾, 3/2, … • -2, -4, -8, -16, …

  9. Write the first 3 terms of the Geometric Sequence • a1 = 24, r = ½ • a1 = 24 means that the first term in your sequence is 24. • r = ½ means that the common ratio is ½. • You will multiply each term by½ in order to get the next term in the sequence. • The first 3 terms of the sequence are: • 24, 12, 6

  10. Write the first 3 terms of the Geometric Sequence. • a1 = 4, r = 2 • a1 = 6, r = 1/3 • a1 = 12, r = -1/2 4, 8, 16 6, 2, 2/3 12, -6, 3

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