Name
Class
Date
Reteaching 11-5
Geometric Series
OBJECTIVE: Finding the sum of a finite and of an
infinite geometric series
•
MATERIALS: None
The sum of a finite geometric series is the sum of the terms of a
geometric sequence. This sum can be found by using the formula
a (1 2 r n)
Sn 5 1 1 2 r , where a1 is the first term, r is the common ratio, and
n is the number of terms.
The sum of an infinite geometric series with ∆r« 1 is found by using
a
the formula S 5 1 , where a1 is the first term and r is the common
1 2 r
ratio. If ∆r« 1, then the series has no sum.
All rights reserved.
•
Example
a1 = 8
a1 is the first term in the series.
r = 16 5 32 5 64 5 128 5 2
8
32
16
64
Simplify the ratio formed by any two consecutive
terms to find r.
n = 10
n is the number of terms in the series to
be added together.
S10 =
=
8(1 2 210)
122
Substitute a1 ≠ 8, r ≠ 2, and n ≠ 10 into the
formula for the sum of a finite geometric series.
8(21023)
21
Simplify inside the parentheses.
= 8184
Simplify.
Exercises
Evaluate the finite series for the specified number of terms.
1. 3 + 12 + 48 + 192 + . . . ; n = 6
3. -10 - 5 - 2.5 - 1.25 - . . . ; n = 7
2. 8 + 2 + 12 1 18 + . . . ; n = 5
4. 10 + (-5) + 25 1 a2 45b + . . . ; n = 11
Evaluate each infinite geometric series.
5. 10 + 5 + 2.5 + . . .
2 2 4 1 ...
6. -1 + 11
121
7 1 49 1 . . .
7. 14 1 32
256
2 2 ...
8. 12 2 15 1 25
1 2 1 1 ...
9. 2 61 1 12
24
1 ...
10. 20 + 16 + 64
5
11. 12 1 4 1 43 1 . . .
12
1 2 ...
12. 14 2 18 1 16
Lesson 11-5 Reteaching
2 1 2 1 ...
13. 32 1 15
75
Algebra 2 Chapter 11
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Find the sum of the first ten terms of the series
8 + 16 + 32 + 64 + 128 + . . .