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9 th Tab Chapter 9

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Sequences 9.1-9.3

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What is n? n is the number spot of the term in a sequence. n 3 is the third number in the sequence (list) A n the result for the last term or the term you are looking to find.

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Sequence Formulas Arithmetic Adding----uses a common difference Formula: a n =a 1 +(n-1)d Geometric Multiplying----uses a common ratio Formula: a n =a 1 *r (n-1)

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C

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Find the n th term of a sequence when a written description of the sequence is given. What is the seventh term of the geometric sequence with a first term of 729 and a common ratio of ?

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B

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H

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H

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A

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390, 625

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J

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Find the missing term of the arithmetic sequence , 25, ___, 53,

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Find the missing terms in the geometric sequence 5, 10,___, ___, 80,

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$135

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Class work

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Series 9.4-9.5

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Summation- Adding up the sequence Sigma Notation (SUM) End Start Formula

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Series S n the sum of all the numbers in a sequence formulas are on the formula sheet.

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D

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G

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G

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Students need additional practice finding the sum of a geometric series, particularly when the common ratio is negative. Find the sum of this series.

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Recursive http://www.regentsprep.org/Regents/math/algtrig/AT P3/Recursive.htm http://www.regentsprep.org/Regents/math/algtrig/AT P3/Recursive.htm

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A runner begins training by running 5 mi. one week. The second week she runs a total of 6.5 mi. The third week she runs 8 mi. Assume this pattern continues. 1. How far will she run in the tenth week? 2. At the end of the tenth week, what will be the total distance she has run since she started training? 3. Express the total distance with summation notation ().

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Suppose on Jan. 1 you deposit $1.00 in an empty piggy bank. On Jan. 8 you deposit $1.50; on Jan. 15 you deposit $2.00; and each week thereafter you deposit $0.50 more than the previous week. 1. What kind of sequence do these deposits generate? 2. What amount will you deposit in the 52nd week? 3. What is the total in the piggy bank at the end of these 52 weeks?