Section 4 - Council Rock School District



Geometric Series

Name Period #

Suppose one evening, you text two people within 5 minutes to spread some gossip. Those two people then both text two new people within 5 minutes to pass along the same gossip, and so on. The number of people texted in each 5 minute period forms a geometric sequence.

TIME |8:00 |8:05 |8:10 |8:15 |8:20 |8:25 |8:30 | |People Contacted |1 |2 |4 |8 |16 |32 |64 | |

The TOTAL number of people that know the rumor now at each time is a SUM of the terms of the geometric sequence.

Definition 1: The sum of the terms of a geometric sequence forms a geometric _______________________.

[pic] 1 person knows the rumor at 8:00 PM (YOU)

[pic] 3 people know the rumor at 8:05 PM

[pic] 7 people know the rumor at 8:10 PM

AND SO ON…

THE FORMULA FOR EVALUATING PARTIAL SUMS:

Ex 1: Using sigma notation to find partial sums of geometric series looks very familiar to what we did with arithmetic series:

Give the sum [pic]

This is equal to 2(3) + 2(32) + 2(33) + …+ 2(312)

So use the formula to give the sum [pic] =

2) Eric calls 4 people within 10 minutes of his son’s birth to pass along the news. They each pass along the news to 4 new people within 10 minutes, and so on. How many total people have heard the news in 1 hour?

3) Write the geometric series 3 + 6 + 12 + … + 96 in sigma notation and find its sum.

3) Write the geometric series 1 + 4 + 16 + … + 4096 in sigma notation and find its sum.

4) Give the sum [pic]

Geometric Series Practice Worksheet 1

Name Period #

Examine the geometric sequence 2, 6, 18, … for questions 1 – 3.

1) Give the common ratio ______________

2) Give the fourth and fifth term ______________

3) Give the partial sums S1, S2, S3, S4

S1 = __________________, S2 = __________________, S3 = __________________, S4 = __________________

Write the word or phrase that correctly completes each statement below.

4) A geometric __________ is the sum of the terms in a geometric ________________.

5) Add the first five terms of a geometric series to find the fifth partial ____________.

Give each sum.

6) the first 15 terms of 2 + 6 + 18 + 54 + … ______________

7) the first 10 terms of 100 + 20 + 4 + … ______________

8) 3 + 6 + 12 + … + 6,144 ______________

Write each geometric series in SIGMA NOTATION and find its SUM.

9) 3 + 12 + 48 + … + 12,288 10) 200 + 100 + 50 + … + 1.5625

Sigma Notation: ___________ Sigma Notation: ___________

Sum: ____________________ Sum: ____________________

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The partial sum of the first n terms of a geometric series with first term a1 and common ratio [pic] is given by the formula:

[pic]

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