13. 11.3 GEOMETRIC SEQUENCES AND SERIES n th Term of a Geometric Sequence In the geometric sequence with first term a 1 and common ratio r , the n th term a n , is
14.
15.
16.
17. 11.3 GEOMETRIC SEQUENCES AND SERIES Sum of the First n Terms of an Geometric Sequence If a geometric sequence has first term a 1 and common ratio r , then the sum of the first n terms is given by where .
22. Find two geometric means between –2 and 54 -2, ____, ____, 54 -2 54 4 NA x The two geometric means are 6 and -18, since –2, 6, -18 , 54 forms an geometric sequence
35. The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. How far does the ball travel? 50 40 32 32/5 40 32 32/5
36. The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. How far does the ball travel? 100 75 225/4 100 75 225/4
37.
38.
39. 11.3 INFINITE GEOMETRIC SERIES Sum of the Terms of an Infinite Geometric Sequence The sum of the terms of an infinite geometric sequence with first term a 1 and common ratio r , where –1 < r < 1 is given by .