Download presentation

Presentation is loading. Please wait.

Published byBethanie Grant Modified over 6 years ago

1
11.4 Geometric Sequences

2
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

3
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….)

4
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?

5
Deriving a formula for the n th partial sum of a geometric sequence

6
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.

7
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.

8
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.

Similar presentations

© 2022 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google