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11.2 Arithmetic Sequences Warm up: 1.) Find the equation of a line in slope intercept form that passes through (8, 50) and slope is ¼. 2.) Find the equation of a line in slope intercept from that passes through the two points (6, 10) and (21, 55) Arithmetic Arithmetic SSequence equence: a sequence where the difference between consecutive terms is constant, denoted by d. Ex: Decide whether each sequence is arithmetic. a) −3, 1, 5, 9, 13, … b) 2, 5, 10, 17, 26, … c) −10, −6, −2, 0, 2, 6, 10, … d) 5, 11, 17, 23, 29, … e) 1, 1, 2, 3, 5, 8, … f) 32, 16, 8, 4, … Ex: Write a rule for the nth term of the sequence −2, 1, 4, 7, …. Then find a20. (Graph then make an x/y chart to help see a pattern…what do you notice?) Rule for an Arithmetic sequence: the nth term of an arithmetic sequence can be determined using the formula below… an = dx + b Ex: Ex: Write a rule for the nth term of the sequence. a) 50, 44, 38, 32, …. Then find a18 b) 32, 47, 62, 77, …. Then find a12 c) 17, 11, 5, −1, −7, …. Then find a15 Ex: Ex: Finding the nth term given a term and the common difference (Hint: Think of finding an equation using the slope and a given point.) a) One term of an arithmetic sequence is a13 = 30. The common difference is d = 3 . 2 b) One term of an arithmetic sequence is a8 = 50. The common difference is d = 0.25 . c) One term of an arithmetic sequence is a20 = −111. The common difference is d = −6 . d) One term of an arithmetic sequence is a2 = 18. The common difference is d = 18 . Ex: Ex: Finding the nth term given two terms. (Hint: Think about how to find the equation of a line given two points.) a) Two terms on an arithmetic sequence are a6 = 10 and a21 = 55. Then find n when an = 40. b) Two terms on an arithmetic sequence are a5 = 10 and a30 = 110. Then find n when an = −2. c) Two terms on an arithmetic sequence are a8 = 12.5 and a15 = 30. Then find n when an = 50