1)I will write a few numbers that follow a pattern (I won’t tell you what the pattern is)

2)You write the next number that you think follows the pattern

3)I will say if your number does or does not follow my pattern

4)Guess the pattern I had in mind

Number Game #1

Let’s look closer at the second set of numbers we looked at:

1, 3, 7, 5, 9

• If the first is 1, the second number is 3, and so fourth; what will the 7’th number be and how do you know?

• What will the 50’th number be? A sequence of numbers is an ordered list of

numbers that follows a specific pattern.

We will consider a specific type of sequence called arithmetic sequence.

This type of bullet will mean an important definition (worth writing down)

Arithmetic Sequences – have a common difference, d, such that each term in the sequence is the sum of the previous term and d.

An arithmetic sequence is always a ‘plus’ or ‘minus’ sequence.

Example:3, 5, 7, 9,…

The common difference, d, is +2 because the numbers increase by 2.

Definition

Arithmetic SequenceExamples Non-

Examples2, 4, 6, 8, 10 2, 4, 8, 165, 2, -1, -4, -7 1, 3, 6, 10, 150.5, 1, 1.5, 2, 2.5

1, -2, 3, -4

1, 3, 9, 27

d= +2

d= 3d= +0.5d= +

The Explicit Formula for an arithmetic sequence is:

Example Find the 22’nd term for the given sequence: 5, 2, -1, -4

1) common difference is: _______2) The first term is: ________3) The term I want is: __________4) The equation is:____________

Find the 56’th term of the sequence:

4.2, 5.6, 7, 8.4, …

Find the 203’rd term of the sequence:-1, -100, -199, -299,…

If the 100’th term in a sequence is 50 and the common difference is 2.5. What is the first term ()?

The School library charges a $1 fine for the first day a book is overdue. The charge is 55 cents for each day after that.

If you return a book 23 days late, how big will your fine be?

Word Problem