Name the next number in the sequence: a) 1, 3, 9, 27, … b) 1, 5, 25, 125, …

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Presentation transcript:

Name the next number in the sequence: a) 1, 3, 9, 27, … b) 1, 5, 25, 125, …

 SWBAT identify and generate geometric sequences.  SWBAT relate geometric sequences to exponential functions.  Students will look for and make use of structure.

 In a geometric sequence, the first term is nonzero and each term after the first is found by multiplying the previous term by a nonzero constant r called the common ratio.  The common ratio can be found by dividing any term by its previous term.

A) 256, 128, 64, 32 Find the ratios of consecutive terms: B) 4, 9, 12, 18 Find the ratios of consecutive terms:

a) 1, 3, 9, 27, … b) -20, -15, -10, -5, … c) 2, 8, 14, 22, …

Find the next three terms in each geometric sequence. a) 1, -4, 16, -64,… Find the common ratio: Multiply each term: B) 9, 3, 1, 1/3, …

Find the next three terms: a) -3, 15, -75, 375, … b) 24, 36, 54, 81,…

Position, n1234…n Term, a n a1a1 a2a2 a3a3 a4a4 …a 1 r n-1 The first term in the sequence is a 1 The common ratio is r. The variable n can be any positive integer. The nth term can be found by a 1 r n-1

a) Write an equation for the nth term of the sequence: -6, 12, -24, 48, … b) Find the ninth term in the sequence.

Write an equation for the nth term of the geometric sequence 96, 48, 24, 12, … Then find the tenth term of the sequence.

 The NCAA women’s basketball tournament begins with 64 teams. In each round, one half of the teams are left to compete, until only one team remains. Draw a graph to represent how many teams are left in each round.

A tennis ball is dropped from a height of 12 feet. Each time the ball bounces back to 80% of the height from which it fell. Draw a graph to represent the height of the ball after each bounce.

1) Find the next three terms: 10, 20, 40, … 2) Find the seventh term: -1, 5, -25,… 3) Find the ninth term: 2, 6, 18, … HOMEWORK: TB pg. 441 (14-30 evens; 43-46)