Arithmetic and Geometric 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 Rule: multiply by 1/5

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

Determine if the sequence is Arithmetic Determine if the sequence is Arithmetic. If so, find the common difference. Yes. d = 2 No Yes, d = 1/9 2/9, 3/9, 4/9, 5/9, 6/9, … Yes. d =-7 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, …

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

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

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

Determine if the sequence is Geometric. If so, find the common ratio. -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, … No Yes. r = 3 Yes. r = -1 Yes. r = 1.5 Yes. r = 2 3/16, 6/16, 12/16, 24/16 Yes. r = 2

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 by ½ in order to get the next term in the sequence. The first 3 terms of the sequence are: 24, 12, 6

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