This document introduces arithmetic sequences, which are sequences that follow a specific pattern where each term is the sum of the previous term and a common difference. It provides examples and non-examples of arithmetic sequences, and defines the explicit formula used to find any term in an arithmetic sequence based on knowing the first term and common difference. It then provides examples of using the formula to find specific terms in given arithmetic sequences.

1. 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

2. 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)

3.  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.

4. Examples Non-Examples
2, 4, 6, 8, 10 2, 4, 8, 16
5, 2, -1, -4, -7 1, 3, 6, 10, 15
0.5, 1, 1.5, 2,
2.5
1, -2, 3, -4
1
2
,
3
4
, 1,
5
4
1, 3, 9, 27
d= +2
d= −3
d= +0.5
d= +
1
4

5.  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:____________

6. 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
(𝑎1)?

7. 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?