Download 11pc sec 1.4 – Geometric Series

Pre-Calculus 11
Section 1.4: Geometric Series
Date: _____________________
Page 1 of 4
Definition:
A geometric series is the _____________ of the terms of a _______________________________.
Investigate: On Monday, Mr. Lee decided to get his own Facebook page. He initially two friends join
his group. On Tuesday, all 3 of his relatives had 3 of their friends visit Mr. Lee’s profile. On
Wednesday, each of the 9 people on Tuesday had 3 different friends visit Mr. Lee’s Facebook page.
Suppose this continued for 1 week, what would be the total number of people who visited Mr. Lee’s
profile?
Let’s write out the geometric series
S = ________________________________________________
Instead of adding the terms directly, let’s evaluate S as follows.
We will multiply each term of the series by 3 (which is the value of the common ratio r), realign the
above under the original series, and subtract equation (1) from equation (2).
We can use this process to develop a general formula for Sn, the sum of the first n terms of a geometric
series. In general, a geometric series can be written as follows, with rSn.
Summary:
The sum of the first n terms of a geometric series is given by:
Sn 
where “ t1 ” is the first term, “r” is the common ratio, and r  1.
Pre-Calculus 11
Section 1.4: Geometric Series
Date: _____________________
Page 2 of 4
Example 1: Determine the sum of 12 terms of the geometric series:
1 1 1 ...

a) S  6 18  54  ...
b) 1  
3 9 27
Example 2: Determine the sum of the following geometric series 2  4  8  ...  1024 . You may
want to try to do this two ways!
Pre-Calculus 11
Section 1.4: Geometric Series
Date: _____________________
Page 3 of 4
Example 3: A ball is dropped from a height of 2 metres. After each bounce, it rises to 70% of its
previous height. What is the total vertical distance travelled by the ball when it hits the floor for the 6th
time?
Pre-Calculus 11
Section 1.4: Geometric Series
Date: _____________________
Page 4 of 4
Example 4: A doctor prescribes 200 milligrams of medication on the first day of treatment. The
dosage is halved on each successive day for two weeks. To the nearest milligram, what is the total
amount of medication administered?
th
Example 5: Determine the n term, and the sum of the first n terms of the geometric sequence which
has 2, 6, and 18 as its first three numbers. Your answers should involve “n”.