ࡱ>  "_ /bjbjzXzX 4,2@\2@\/ <$^ffffmmm%''''''$T"KmNmmmKff`yyym ff%ym%yyyfP~Tw yv0y#|#y#ymmymmmmmKK|mmmmmmm#mmmmmmmmm> Z: Math 1: Sequences Name_____________________________________ 5.1-1 Notes: Arithmetic Sequences Sequence: another name for an ________________________________________. Arithmetic Sequence: formed by ___________________ a fixed number to each previous term.  (ex) 4, 5, 14, 23   SHAPE \* MERGEFORMAT  _______________  +_____ +_____ +_____ ___________________________________ *The best way to find the common difference is to subtract the _______________ term from the ________________________ term. *NOTE: The common difference will be ___________________________ if the sequence is increasing and _________________________ if the sequence is decreasing. Example 1: Find the common difference of each arithmetic sequence. (a) 7, 3, 1, 5, . . . (b) 8, 3, 2, 7, . . . (c) 5, 2, 1, 4, . . . Example 2: Find the next two terms in each sequence. (a) 20, 14, 8, 2, _____, _____ (b) 0.7, 1.5, 2.3, 3.1, _____, _____ (c) 5, 4, 13, 22, _____, _____ Example 3: Let n = the term number in the sequence and an = the value of the nth term of the sequence. (a) Find the first, fifth, and tenth terms of the sequence that has the rule an = 12 + (n 1)( 2). (b) Find the first, sixth, and twelfth terms of the sequence that has the rule an = 5 + (n 1)( 3). (c) Find the first, fourth, and eleventh terms of the sequence that has the rule an = 7+ (n 1)( 4). Notes: Geometric Sequences Geometric Sequence: formed by ___________________________ a fixed number to each previous term. (ex) 2, 10, 50, 250   SHAPE \* MERGEFORMAT   _____ _____ _____ ____________________________ *The best way to find the common ratio is to divide the _________________ term by the _____________ term and simplify. Example 1: Find the common ratio of each geometric sequence. (a) 3, 12, 48, 192, . . . (b) 3, 6, 12, 24, . . . *NOTE: The common ratio is ___________________________ if all terms in the sequence are all positive OR all negative. *NOTE: The common ratio can be a ___________________________! (c) 750, 150, 30, 6, . . . (d) 88, 44, 22, 11, . . . *NOTE: The common ratio is ___________________________ if the signs of the terms in a sequence alternate between positive and negative. (e) 2, 6, 18, 54, . . . (f) 3, 15, 75, 375, . . . Example 2: Find the next three terms in each sequence. (a) 1, 3, 9, 27, _____, _____, _____ (b) 120, 60, 30, 15, _____, _____, _____ Example 3: Let n = the term number in the sequence and an = the value of the nth term of the sequence. (a) Find the first, fifth, and tenth terms of the sequence that has the rule  EMBED Equation.3 . (b) Find the first, sixth, and twelfth terms of the sequence that has the rule  EMBED Equation.3 . 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