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Arithmetic Sequences

Geometric Sequences

Arithmetic Series

Geometric Series

Sigma Notation

Mathematical Induction

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 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 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, …}

Text Box: a = t1 = first term
r = common ratio
n = term number
 

 

 

 

 

 


Definition: The sum of the terms of a Geometric sequence is a Geometric Series.

Text Box: n = the number of terms
t1 = a = the first term
r = the common ratio
Sn = the sum of the series
                                                                                                           

Text Box:
 

 

 

 

 

 


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 year’s revenue and gains 15% more.  Therefore to get the next year’s revenue, multiply the previous year’s 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:

 

 

 

 

 

 

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