Sequences – Arithmetic
Name _________________
A ________________________ is a pattern of numbers.
Each number in the sequence is called a __________________. Ex: 1, 4, 9, 16, 25, …
Arithmetic Sequences
Look at the pattern of dots below.
1. Describe IN WORDS the pattern that you observe in the designs below.
(I observe …. I notice …. I see
that ….)
2. Construct the next design. How many dots are in design 5?
3. How many dots would be in the 20th design? How do you know???
4. How many dots would be in the nth design? Write an expression. Prove your work
(explain in words, a picture, a table, etc….)!
Arithmetic Sequence – Description:
The number that is __________________ to find the next consecutive term is called the
____________________. Ex. 1: 10.5, 13, 15.5, 18, 20.5, …
Ex. 2: 30, 25, 20, 15, …
Sequences – Arithmetic
Name _________________
More examples and non-examples:
Arithmetic
Not arithmetic
There are two main ways we express sequences:

Using a recursive formula –

Using an explicit formula –
* When might it be more useful to use a recursive formula? … an explicit formula?
Example 1: Given a1 = 3
an = an-1 + 4
Find a2 =
a3 =
a4 =
Example 2: Given b1 = -2
bn = bn-1 - 3
Find the first FIVE terms.
Create your own sequence with a common difference of 4! _____________________
Example 3: What is the 100th term of the arithmetic sequence that begins 6,11,…?
Ex. 4: What is the 46th term of the arithmetic sequence that begins 3,5,7,…?
Ex. 5: What are the second and third terms of the arithmetic sequence 100, ___, ___, 82,…?
Ex. 6: What are the three missing terms in the arithmetic sequence? 28, ____, _____, _____, 8
Sequences – Arithmetic
Name _________________
Example 7: Given that a1 = 23 and a4 = -1, write a formula for the arithmetic sequence.
Example 8: Given that a1 = 34 and a5 = 58, write a formula for the arithmetic sequence.