Geometric Sequences: Properties, Formulas, and Examples, Study notes of Pre-Calculus

Download Geometric Sequences: Properties, Formulas, and Examples and more Study notes Pre-Calculus in PDF only on Docsity!

Math 30P

Geometric Sequences

Believe it or not we studied sequences in grade 10

A sequence is a set of numbers in a definite

order which are written separated by commas

A common way to define a sequence

is in terms of the n

th

term formula

Ex # Write the next two terms of the following sequence and

describe a rule which can be used to form the sequence

a) 1, 3, 5, 7, ...

b) 2, 4, 8, 16, ...

c) 2, 3, 5, 7, 11, ...

d) 1, 1, 2, 3 ,5, ...

Ex #

List the first three terms of the sequence

t

n

= 3n

2

n a)

b) Determine the 8

th

term of the seqeunce t

n

= 4n

2

Types of Sequences

Arithmetic

terms are created by

adding the same number to

the preceding term

they have a common difference

(6 above)

Math 10P

t

n

= t

1

• (n1)d

Others

Geometric

terms are created by

multiplying the same number to

the preceding term

They have a common ratio

(2 above)

Find common ration by

t

2

t

1

Developing the n

th

term formula

Consider the following sequence 3, 6, 12, 24, ...

t

1

t

2

t

3

t

4

t

5

t

6

1

The general formula for a geometric sequence

t

n

= ar

n

a = t

r = common ratio

n = position of the term being considered

Ex#5: Determine the general term (n

th

term formula) and

calcualte the seventh for each of the following

a) 32, 16 ,8,...

b) 1/3 , 1/6 , 1/12, ....

Given the geometric sequence with t 4

=54 and t

7

=1458, find the:

first term

common ratio

general term

a)

b)

c)

x, x + 5, x + 9

are the first three terms in a geometric sequence. Determine

the exact value of each term

Ex #

• PAges 164168 #