Sequences and Series The study of order….. Suppose you were the “Fry-Guy” at McDonalds for the summer… Summer jobs?

Sequences and Series

The study of order…..

Suppose you were the “Fry-Guy” at McDonalds for the summer…

Summer jobs?

The Graph of your bank account would look like:

At your job, you were able to bank $125.00 per week for 8 weeks

week 1 2 3 4 5 6 7 8

Total 125 250 375 500 625 750 875 1000

This relationship can be represented in different ways

Week

$

1 2 3 4 5 6 7 8

1000

0

Your pay can also be represented with a

function(where we begin)

To do this, we need to examine the pattern of the numbers

1 2 3 4 5 6 7 8

Examine the following patterns to predict what

the next symbol will be….

O T T F F …..

M T W T F S ….

JF M A M …

Given any pattern, the simplest progression will be the implication.

These examples are called Sequences

8 4 2 1 …

1 8 27 …

0 2 6 12 …1 3 5 7 9 …

2 4 8 1632 …

• A number sequence is a set of numbers, usually separated by commas, arranged in an order.

• The first term in t1, the second term t2, and so on…

• Write the sequence given the formula for the nth term

• tn = 3n – 2

• Find the 10th term

• Write the formula for the given sequence

• 4,7,10,13

• Pg 433• 1[a,c,e]• 2[a,c,e,g]• 3,4 [odd]• 5a

• Do not find the formula

The implicated sum of the terms of any sequence is called a

SERIES

• SERIES1+ 3+ 5+ 7+9 …1 3 5 7 9 …• SEQUENCE

These sequences can be divided into 2 groups….any suggestions?

8 4 2 1 …

0 5 10 15 …1 3 5 7 9 …

2 4 8 16 32 …

+

X

Arithmetic

8 4 2 1 …

1 3 5 7 9 …

Geometric

Add 2 every step

Multiply by 0.5

A Geometric Sequence

•What if your pay was doubled every week?

•What would the results look like in that case?

Weeks Pay1 125

2 250 3 500 4 1000 5 2000 6 4000

7 8000 8 16000

Week

$

1 2 3 4 5 6 7 8

16000

0

1 3 5 7 9 …

•In an arithmetic sequence, terms are generated using a constant common difference

Example1) The sequence 2,9,16… is

given; determine the 20th term.

A Mechanical solution-

=2,9,16,23,30,37,…135

Pg 121,2 4,5,7,8,912,14,15