Figure out how to work with infinite series when i=0 vs i=1 Slide 12

Geometric Sequences and Series Objectives: To recognize a pattern as a geometric sequence To formulate the sequence equation as a function of n To sum up a finite OR INFINITE geometric sequence

Is the following sequence arithmetic 10, 20, 40, 80, 160,… NO!! The difference from one term to the next is NOT a constant difference But, something is going on here

Vocabulary Geometric Sequence: A sequence where the ratio of consecutive terms are the same Again, work RIGHT TO LEFT r is a common ratio

#1 Determine if the sequence is geometric 1.5; 15; 45;

Finding the equation for the nth term of a geometric sequence A geometric sequence of an equation is given by a n = a 1 r n-1 r is the common ratio Consider 2, 4, 8, 16, …

Example # Give the first five terms of the geometric sequence a 1 = 2 r= 3

#21 Write the first five terms of the geometric sequence, determine the common ratio and write a n as a function of n a 1 = 64 a k+1 =

If r is negative, you will have alternating signs!! #24

Determining a Geometric Series In other words, adding the terms of a geometric sequence Two types of sums/ series: 1.) Infinite Geometric Series 2.) Finite Geometric Series

The Sum of an Infinite Geometric Series Condition: This can only be done if Notation and how to calculate an INFINITE GEOMETRIC SERIES/ SUM

Proof

Consider …….

Why are we able to add an infinite number of terms? Consider (82ish)

#78

The Sum of a Finite Geometric Series The sum of a finite geometric sequence

BEWARE of START INDEX NUMBER 52 vs 60

Homework Pg. 640 #1-7; 11-14; 21-24; 28-38(even); (evn); ; 78-88(even); 91-92; 98; 99; 101