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UNIT
8 :
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 t1 , t2 , t3 , 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. t6
= 32 x 2 = 64 etc.
·
The
formula for the general term or nth term is tn = arn-1.
·
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 S9 , 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 t1
= -2 and t5 = -32. Find S12.
5. A certain geometric series has r = -3 and S8
= -3280. Find a.
6. A certain geometric series has t3
= 12 and t8 = 384. Find S11.
Solutions:
1. In each of the following geometric series,
determine S9 , 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 S9 = ?
a = 7 r = -2 n = 9 S9 = ?
a = 2 r = 5 n = 9 S9 = ?
a = 64 n = 5 S5 = ?
a = 2 d = 0.5 n = 60 Sn = ?
2. Find the sum of the following geometric
series.
Solutions:
a = 4 r = 2 n = ? tn = 1024 Sn = ?
a = -2 r = 3 n = ? tn = - 4374 Sn = ?
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 t1
= -2 and t5 = -32. Find S12.
Solution:
5. A certain geometric series has r = -3 and S8
= -3280. Find a.
Solution:
6. A certain geometric series has t3
= 12 and t8 = 384. Find S11.
Solution:
