Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?

Geometric Sequences Geometric Sequence– a sequence whose consecutive terms have a common ratio.

A sequence is geometric if the ratios of consecutive terms are the same. Geometric Sequence ratio The number r is the common ratio.

2, 4, 8, 16, …, formula?, … Ex. 1 12, 36, 108, 324, …, formula?, … 1, 4, 9, 16, …, formula?, … Are these geometric? Yes 2 n Yes 4(3) n No n 2 No (-1) n /3

Finding the nth term of a Geometric Sequence a n = a 1 r n – 1

Ex. 2b Write the first five terms of the geometric sequence whose first term is a 1 = 9 and r = (1/3).

Ex. 3 Find the 15 th term of the geometric sequence whose first term is 20 and whose common ratio is 1.05 a n = a 1 r n – 1 a 15 = (20)(1.05) 15 – 1 a 15 =

Ex. 4 Find a formula for the nth term. What is the 9th term? 5, 15, 45, … a n = 5(3) n – 1 a 9 = 5(3) 8 a 9 = a n = a 1 r n – 1

Ex. 5 The fourth term of a geometric sequence is 125, and the 10 th term is 125/64. Find the 14 th term. (Assume all terms are positive) a 4 = 125 a 10 = a 10 = a 4 r 6 a 14 = a 10 r 4 a 14 =

sum of a finite geometric series

Ex. 6 Find the sum of the first 12 terms of the series 4(0.3 )n = 4(0.3) 1 + 4(0.3) 2 + 4(0.3) 3 + … + 4(0.3) 12 = 1.714

Ex. 7 Find the sum of the first 5 terms of the series 5/ … r = 5/(5/3) = 3 = 605/3

What are your questions? Homework: Page 771 #16-22 even, 26, 27, 30, 32, 37, 38