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PDF Arithmetic Sequences.notebook Warm Up: Find the next two numbers in the patterns. 1. 26, 34, 42, 50, ... 2. 2, ‐4, 8, ‐16, ... 3. ‐11, ‐16, ‐21, ‐26, ... 4. 7, 6.5, 6, 5.5, ... 5. 5, 20, 80, 320, ... 6. 2, 5, 9,14, 20 November 14, 2016 Sequences: Two Major Types Arithmetic Geometric changes according to a common difference, d changes according to a common ratio, r Nov 72:39 PM Apr 239:28 PM For the patterns you looked at before decide if they are arithmetic, geometric or neither. If arithmetic find "d" and if geometric, find "r". 1. 26, 34, 42, 50, ... 2. 2, ‐4, 8, ‐16, ... 3. ‐11, ‐16, ‐21, ‐26, ... 4. 7, 6.5, 6, 5.5, ... 5. 5, 20, 80, 320, ... 6. 2, 5, 9,14, 20 Arithmetic Sequences Sequence: An ordered list of numbers that often forma a pattern. Term of a sequence: Each number in the list. Arithmetic Sequence: The difference between consecutive terms is constant. This difference is called the common difference. Is the sequence arithmetic? If so what is the common difference? Nov 72:39 PM 3,8,13,15,... 10,4,2,8,... 6,9,13,17,... 2,2,2,2,... Feb 153:20 PM Recursive Formula: A function rule that relates each term of a sequence after the first to the ones before it. An+1 = An + d , Where: an+1 is the next term a is the now term n d is the common difference Explicit Formula: A function rule that relates each term of a sequence to the term number. An = A1 + (n-1)d Example: Consider the sequence 7,11,15,19,... You can use the common difference of this arithmetic sequence to write a recursive formula. The common difference is 4 Let n=the term number in the sequence. where th An: The n term A1: The first term n: term number d: common difference th Let An = the value of the n term of the An+1 =An + 4 sequence. A3=A2 + 4 = 11 + 4 = 15 You try: 1.) 3,9,15,21,....... 2.) 10, 4, 2, 8...... Feb 153:21 PM Feb 153:21 PM 1 PDF Arithmetic Sequences.notebook November 14, 2016 Arithmetic n th Term Explicit Formula: A subway pass had a starting value of $100(n=0). After one ride, the value of the pass is $98.25. After two rides, its value is $96.50. After 3 rides its remaining value is $94.75 Write an explicit formula to represent the remaining value on the card as an arithmetic sequences. What is the value of the pass after 15 rides? Example: Write an explicit formula for the sequence 23,35,47,59... Find 10th term of the sequence. How many rides can be taken with the pass? Nov 73:07 PM Writing an Explicit Formula From a Recursive Formula: An arithmetic sequence is represented by the recursive formula An+1 = An + 12. If the first term is 19, write the explicit formula. A1 = n = d= Formula: Feb 153:21 PM Writing a Recursive Formula From an Explicit Formula: An arithmetic sequence is represented by the explicit formula An = 32 + (n-1)(22). What is the recursive formula? The first term: A 1 = 32 The common difference is 22 What would be the 15th term? What would be the 100th term? Try: Write an explicit formula for the sequence: 1. An = An1 +2 where A(1) = 21 2. An=An1 + 7 where A(1) = 2 Feb 153:56 PM An+1 = A n +22 Try: Write a recursive formula for the sequence: 1. A(n) = 76 + (n - 1)(10) 2. A(n) = 1 +(n-1)(3) Feb 154:02 PM Homework: Page 269 # 228 even, 3440 even, 5054 even, 55, 6468 even Nov 63:10 PM 2
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