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Published byMelanie Watson Modified over 9 years ago
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Sequences and Series
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Sequence There are 2 types of Sequences Arithmetic: You add a common difference each time. Geometric: You multiply a common ratio each time.
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Arithmetic Sequences Example: {2, 5, 8, 11, 14,...} Add 3 each time {0, 4, 8, 12, 16,...} Add 4 each time {2, -1, -4, -7, -10,...} Add –3 each time
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Arithmetic Sequences Find the 7 th term of the sequence: 2,5,8,… Determine the pattern: Add 3 (known as the common difference) Write the new sequence: 2,5,8,11,14,17,20 So the 7 th number is 20
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Arithmetic Sequences When you want to find a large sequence, this process is long and there is great room for error. To find the 20 th, 45 th, etc. term use the following formula: a n = a 1 + (n - 1)d
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Arithmetic Sequences a n = a 1 + (n - 1)d Where: a 1 is the first number in the sequence n is the number of the term you are looking for d is the common difference a n is the value of the term you are looking for
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Arithmetic Sequences Find the 15 th term of the sequence: 34, 23, 12,… Using the formula a n = a 1 + (n - 1)d, a 1 = 34 d = -11 n = 15 a n = 34 + (n-1)(-11) = -11n + 45 a 15 = -11(15) + 45 a 15 = -120
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Arithmetic Sequences Melanie is starting to train for a swim meet. She begins by swimming 5 laps per day for a week. Each week she plans to increase her number of daily laps by 2. How many laps per day will she swim during the 15 th week of training?
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Arithmetic Sequences What do you know? a n = a 1 + (n - 1)d a 1 = 5 d= 2 n= 15 t 15 = ?
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Arithmetic Sequences t n = t 1 + (n - 1)d t n = 5 + (n - 1)2 t n = 2n + 3 t 15 = 2(15) + 3 t 15 = 33 During the 15 th week she will swim 33 laps per day.
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Arithmetic Series The sum of the terms in a sequence are called a series. There are two methods used to find arithmetic series: Formula Sigma Notation
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Find the 14 th term of the arithmetic sequence with first term of 5 and the common difference is –6. t n = a + (n – 1) d t 14 = You are looking for the term! List which variables from the general term are provided! The 14 th term in this sequence is the number - 73! a = 5 and d = -6 5 -6 = 5 + (13) * -6 = 5 + -78 = -73
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In the arithmetic sequence 4,7,10,13,…, which term has a value of 301? t n = a + (n – 1) d You are looking for n! The 100 th term in this sequence is 301!
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