Iterative Patterns Arithmetic and Geometric Define 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, … Rule: add 2 96, 92, 88, 84, 80, … Rule: multiply by 2 Rule: subtract 4 625, 125, 5, … 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: d=3 › 3, 6, 9, 12, 15… › 85, 90, 95, 100, 105, … d = 5 › 5, 3, 1, -3, -5, … d = -2

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

Write the first 5 terms of the Arithmetic Sequence. � a 1 = 2, d = 1 � a 1 = 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. 1. a 1 = 3, d = 7 1. 3, 10, 17, 24, 31 2. a 1 = 0, d = 0. 25 2. 0, 0. 25, 0. 75, 1 3. 4. a 1 = 100, d = -5 a 3 = 6, d = -4 3. 100, 95, 90, 85, 80 4. 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, … Rule: r = 2 › 1000, 10, 1, 0. 1, … Rule: r = 1/10 › 81, 27, 9, 3, … Rule: r = 1/3

Determine if the sequence is Geometric. If so, find the common ratio. 1. -4, -2, 0, 2, 4, … 1. No 2. 2, 6, 18, 54, 162, … 2. Yes. r = 3 3. 2/ 3. Yes. r = -1 4. 1, 1. 5, 2. 25, 3. 375, … 5. 3/ 6. -2, -4, -8, -16, … 2/ , - 2/ , … , 3 3 3/ , ¾, 3/ , … , 16 8 2 4. Yes. r = 1. 5 5. Yes. r = 2 3/ , 6/ , 12/ , 24/ 16 16 6. Yes. r = 2

Write the first 3 terms of the Geometric Sequence a 1 = 24, r = ½ � a 1 = 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. 1. a 1 = 4, r = 2 1. 4, 8, 16 2. 1/ 2. 6, 2, 2/3 3. a 1 = 6, r = a 1 = 12, r = 3 - 1/ 3. 12, -6, 3 2