9.3 Geometric Sequences and Series

9.3 Geometric Sequences A sequence is geometric if the ratios of consecutive terms are the same. This common ratio is r. Take any two consecutive terms and divide them.

Write the first five terms of the geometric sequence whose first term a 1 = 3 and common ratio r = 2. a 1 = 3 a 2 = 3(2 1 ) = 6 a 3 = 3(2 2 ) = 12 a 4 = 3(2 3 ) = 24 a 5 = 3(2 4 ) = 48 What is the 10 term? What is the nth term of a geometric sequence? a n = a 1 r n-1 a 10 = 1536

Find the 15th term of the geometric sequence whose first term is 20 and whose common ratio is a 15 = 20(1.05) 14 = Find the 12th term of the geometric sequence 5, 15, 45, ……. First, find a 1 and r. a 12 = 5(3) 11 = 885,735

The 4th term of a geometric sequence is 125, and the 10th term is 125/64. Find the 14th term. To solve this problem let’s let the 4th term now be the first term, the 10th term the 7th term, and the 14th term be the 11th term. a 1 = 125, a 7 = 125/64, a 11 = ? a 7 = a 1 r 6 Now we can find a 11

The Sum of a Finite Geometric Sequence Find the following sum. To find the sum we must find a 1, r, and n. What are they?

The Sum of an Infinite Geometric Sequence If |r| < 1, then the sum of an infinite geometric sequence is

Find the sum of the following infinite geometric sequence. 4, 4(.6), 4(.6) 2, 4(.6) 3,….,4(.6) n-1 What is a 1 and r?