11.4 Geometric Sequences

11.4 Geometric Sequences and Series geometric sequence If we start with a number, a 1, and repeatedly multiply it by some constant, r, then we have a geometric sequence: a 1, a 1 r, a 1 r 2, a 1 r 3, a 1 r 4,…. The n th term of a geometric sequence is given by The number r is called the common ratio

11.4 Geometric Sequences and Series (Example 2) Find the 8 th term of the geometric sequence: 5, 15, 45, … Solution: Use formula, a n = a 1 r ( n – 1) a 1 = r = n = (Now work Example 3 in text….)

Geometric Series geometric series The sum of the terms of a geometric sequence is called a geometric series. For example: is a finite geometric series with common ratio r. What is the sum of the first n terms of a finite geometric series?

Deriving a formula for the n th partial sum of a geometric sequence

11.4 Geometric Sequences and Series infinite geometric series The sum of the terms of an infinite geometric sequence is an infinite geometric series. For some geometric sequences, S n gets close to a specific number as n gets large. This number becomes the limit of the sum of the infinite geometric sequence. When |r|<1, the limit or sum of an infinite geometric series is given by.

11.4 Geometric Sequences and Series You should be able to: Identify the common ratio of a geometric sequence, and find a given term and the sum of the first n terms. Find the sum of an infinite geometric series, if it exists.

11.4 Sequences and Series You should be able to: Find terms of sequences given the n th term. Convert between sigma notation and other notation for a series.