2 ADD To get next term MULTIPLY To get next term 2. Geometric Sequences and SeriesArithmetic SeriesSum of TermsGeometric SeriesSum of TermsArithmetic SequencesGeometric SequencesADDTo get next termMULTIPLYTo get next term+ d+ d+ d+ d+ d+ da1a2a3a4a5a6an - 1an r r r r r r
3 Geometric Sequences (Type 2) In geometric sequences, you multiply by a common ratio (r) each time.1, 2, 4, 8, 16, ...multiply by 227, 9, 3, 1, 1/3, ... Divide by 3 which means multiply by 1/3ie
4 The nth term of an geometric sequence is denoted by the formula Where a is the 1st term and r is the common ratioThe sum of the first n terms of a geometric series is foundby using:Note if r>1 then we can use the formulaWhich is more convenient
20 The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 ofit’s height, and continues this pattern until it stops. How fardoes the ball travel?504040323232/532/5
21 The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 ofit’s height, and continues this pattern until it stops. How fardoes the ball travel?1001007575225/4225/4
22 An old grandfather clock is broken An old grandfather clock is broken. When the pendulum is swung it follows a swing pattern of 25 cm, 20 cm, 16 cm, and so on until it comes to rest. What is the total distance the pendulum swings before coming to rest?252520201616
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