“Patterns serve as the cornerstone of algebraic thinking” (Taylor-Cox, 2003, p. 15).
“Algebraic thinking or algebraic reasoning involves forming generalizations from experiences with number and computation, formalizing these ideas with the use of a meaningful symbol system, and exploring the concepts of pattern and function” (Van de Walle, Karp, & Bay-Williams, 2013, p. 258).
Look for a pattern in each of the following numerical, geometric, and alphabetic sequences. Answer the questions, and clearly show your reasoning. When giving “n th term” formulas, simplify the formula.
3.
2.
1. 1, 5, 9, 13, ____ , ____ , ____
Explanation of the pattern:
Is this sequence arithmetic, geometric, or neither of these? _____________________
Find the 1000 th
term.
Find a formula for the n th
term.
5, 10, 20, 40, ____ , ____ , ____
Explanation:
Is this sequence arithmetic, geometric, or neither of these? _____________________
Find the 10 th
term.
Find a formula for the n th
term.
25, 36, 49, 64, 81, 100, 121, 144, ____ , ____ , ____
Explanation:
Is this sequence arithmetic, geometric, or neither of these? _____________________
Find the 25 th term.
Find a formula for the n th
term. (This is tricky; remember that n is the term number – 1 st
, 2 nd
, 3 rd
,. . . . )

4.
_______ , _______ , _______
5.
6. uno, uno, dos, uno, uno, dos, uno, _______ , dos, ________ , _______
1, 8, 27, 64, ____ , ____ , ____
Explanation:
Is this sequence arithmetic, geometric, or neither of these? _____________________
Find the 20 th
term.
7.
8.
9.
10.
Find a formula for the n th
term.
1000, 500, 250, 125, ______ , ______ , ______
Explanation:
P.S. Is this sequence arithmetic, geometric, or neither of these? _____________________
2, 3, 5, 8, 13, ____ , ____ , ____
Explanation:
P.S. These are terms from “the Fibonacci Sequence”. stomp, stomp, clap, whistle, stomp, stomp, _________ , whistle, __________ , stomp, clap, __________
___________ , ___________ , ___________
Explanation:
Is this sequence arithmetic, geometric, or neither of these? _____________________

11.
Explanation:
______________ , ______________ , ______________
Is this sequence arithmetic, geometric, or neither of these? _____________________
12. A, B, C, A, A, B, C, A, ___, ___, ___, A, A, B, . . . What is the 100 th
letter in this sequence? _____
13. Consider the following tile arrangements. How many blue _____ and how many white _____ tiles are in the 50 th
pattern?
14. The years 1992, 1996, 2000, 2004, . . . are Summer Olympic years. When is the next Summer Olympics year? _______
Where will the next Summer Olympics be hosted?
Is the year 2020 a Summer Olympic year?
What about 2030?
15. Write your own patterns problem. Be creative!
* For Fun! 16. Complete the following letter sequence: O, T, T, F, F, S, S , ___ , ___ , ___ , ___ , ___