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Each sequence in the first column is called an ARITHMETIC SEQUENCE because each has a common difference (d). To go from one term to the next, we add the common difference. (The common difference can be _________________ or ____________________. In Sequence #1a, d = ______. In Sequence #2a, d = ______. In Sequence #3a, d = ______. Each sequence in the second column is called a GEOMETRIC SEQUENCE because each has a common ratio (r). To go from one term to the next, we multiply by the common ratio. In Sequence #1b, r = ______. In Sequence #2b, r = ______. In Sequence #3b, r = ______. A sequence is a ______________ whose domain is _________________. Term #1234nValue ( EMBED Equation.DSMT4 )471016 EXPLICIT formula for the nth term of an ARITHMETIC SEQUENCE: EXPLICIT formula for the nth term of a GEOMETRIC SEQUENCE: In this sequence: 5, 9, 13, 17, 21, 25, 29 . What is a3? _______ What is a6? _______ What is a87? _______ Write the explicit formula for each sequence. Then use the formula to find a28 for each sequence. 5, 10, 15, 20, 25, Explicit formula: ______________________________ a28 = 2, 6, 18, 54, Explicit formula: ______________________________ a28 = 50, 48, 46, 44, 42, Explicit formula: ______________________________ a28 = The explicit formulas can be used in multiple ways: 1. In the sequence 8, 19, 30, 41, , which term is 305? 2. A geometric sequence has a1 equal to -2 and a10 equal to -39,366. Find the value of r. Arithmetic Mean: Geometric Mean: Examples: Find the arithmetic mean of 5 and 36. Find the geometric mean of 5 and 45. Arithmetic and Geometric MeanS Examples: Insert 3 arithmetic means between 2 and 34. Insert 4 geometric means between 500 and  EMBED Equation.DSMT4 . RECURSIVE FORMULA: A formula that defines a sequence by relating each term to _________________. ** A recursive formula must have at least ______________ _____________________. Example #1: Write the first 5 terms of the following sequence, which is defined recursively: a1=10 ______ ______ ______ ______ ______ an=an-1+7 Example #2: Write the first 5 terms of the following sequence, which is defined recursively: a1=-6 ______ ______ ______ ______ ______ an+1=5an Example #3: Write a RECURSIVE formula for the sequence below: (Remember it must have 2 parts.) 10, 8, 6, 4, 2, Example #4: Write a RECURSIVE formula for the sequence below: (Remember it must have 2 parts.)  EMBED Equation.DSMT4  Practice Problems: In the arithmetic sequence .7, .9, 1.1, 1.3, , which term is 21.3? If a1=98 and a37=83.6 in an arithmetic sequence, find the common difference d. 3. In the following sequence, find n if an = 686.  EMBED Equation.DSMT4  4. Find the arithmetic mean of 47 and 98. 5. Find the geometric mean of 58 and 9.28. 6. Find the missing terms in the following geometric sequence: , 27, ___, ___, ___,  EMBED Equation.DSMT4 , 7. 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