
UNIT
10 :
SEQUENCES AND SERIES
LESSON 4:
GEOMETRIC SERIES HOMEWORK QUESTIONS
Quick Review:
Geometric
Series:
Recall a sequence such as 2, 4, 8, 16, 32,
is called a Geometric
Sequence. These sequences have the following
properties.
·
Terms
are denoted as t_{1} , t_{2} , t_{3 , }referring
_{ }to term1, term 2,
term 3
·
·
This
ratio is called the common ratio and denoted using the letter r. Here r = 2.
·
The
first term is denoted using the letter a. Here a = 2.
·
Successive
terms are found by multiplying a given term by the common ratio. Eg. t_{6}
= 32 x 2 = 64 etc.
·
The
formula for the general term or nth term is t_{n }= ar^{n1}.
·
Geometric
sequences are exponential functions with domain the natural numbers N
= {1, 2, 3, 4,
}
Definition: The sum of the terms of a
Geometric sequence is a Geometric Series.
Homework
Questions:
1. In each of the following geometric series,
determine S_{9 , }unless otherwise specified .
a) 3 + 6 + 12 +
b) 7 14
+ 28 56 +
c) 2 + 10 + 50 +
[to five terms only]
[to eight terms only]
2. Find the sum of the following geometric
series.
3. Last year InternetCorp had gross revenue of
$500 000. If revenue increases by 15%
per year, find the total revenue achieved by the company after 5 years.
4. A certain geometric series has t_{1}
= 2 and t_{5} = 32. Find S_{12}.
5. A certain geometric series has r = 3 and S_{8}
= 3280. Find a.
6. A certain geometric series has t_{3}
= 12 and t_{8} = 384. Find S_{11}.
Solutions:
1. In each of the following geometric series,
determine S_{9 , }unless otherwise specified .
a) 3 + 6 + 12 +
b) 7 14
+ 28 56 +
c) 2 + 10 + 50 +
[to five terms only]
[to eight terms only]
Solutions:
a = 3 r = 2 n = 9 S_{9} = ?
a = 7 r = 2 n = 9 S_{9} = ?
a = 2 r = 5 n = 9 S_{9} = ?
a = 64
n = 5 S_{5} = ?
a = 2 d = 0.5 n = 60 S_{n} = ?
2. Find the sum of the following geometric
series.
Solutions:
a = 4 r = 2 n = ? t_{n} = 1024 S_{n} = ?
a = 2 r = 3 n = ? t_{n} =  4374 S_{n} = ?
3. Last year InternetCorp had gross revenue of
$500 000. If revenue increases by 15%
per year, find the total revenue achieved by the company after 5 years.
Solution:
The
company maintains 100% of its previous years revenue and gains 15% more. Therefore to get the next years revenue,
multiply the previous years revenue by 115% (1.15 in decimal form).
4. A certain geometric series has t_{1}
= 2 and t_{5} = 32. Find S_{12}.
Solution:
5. A certain geometric series has r = 3 and S_{8}
= 3280. Find a.
Solution:
6. A certain geometric series has t_{3}
= 12 and t_{8} = 384. Find S_{11}.
Solution: