Exercise 3 Page 409

Practice makes perfect

a Let's start by recalling the definition of arithmetic sequences.

Arithmetic Sequence
A sequence in which the difference between consecutive terms is constant is called an arithmetic sequence.

The terms of an arithmetic sequence with first term a_1 and common difference d can be formed as follows.

a_1	a_1
a_2	a_1+d
a_3	a_2+d
a_4	a_3+d
...	...
a_n	a_(n-1)+d

We can conclude that each term in an arithmetic sequence is the sum of the common difference and the previous term. a_1&=a a_n&=a_(n-1)+d

Extra

Example Arithmetic Sequence

Let's investigate the relationship between the terms in the arithmetic sequence with first term a_1=1 and common difference d=1.5.

We can see that each term in this arithmetic sequence is the sum of the common difference 1.5 and the previous term. a_1&=1 a_n&=a_(n-1)+1.5

b Now we will investigate the relationship between the terms in a geometric sequence.



Geometric Sequence



A sequence in which the ratio of any term to the previous term is constant is called a geometric sequence.



The terms of a geometric sequence with first term a_1 and common ratio r can be formed as follows.




 a_1

 a_1


 a_2

 r* a_1


 a_3

 r* a_2


 a_4

 r* a_3


 ...

 ...


 a_n

 r* a_(n-1)

We can conclude that each term in a geometric sequence is the product of the common ratio and the previous term.  
a_1&=a 
a_n&=r * a_(n-1)
        Extra
   Example Geometric Sequence      
 
   Let's investigate the relationship between the terms in the geometric sequence with first term a_1=0.5 and common ratio r=2. 

We can see that each term in the geometric sequence is the product of the common ratio 2 and the previous term. a_1&=0.5 
a_n&=2 * a_(n-1)

Geometric Sequence
A sequence in which the ratio of any term to the previous term is constant is called a geometric sequence.

Subchapter links

Communicate Your Answer p.409

Monitoring Progress p.410-413

Exercises p.414-416

Exercise 3 Page 409

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