 ## Secret Sequences

Mathematics, Algebra and Function, Data Analysis and Probability, Problem Solving

### Objective

Students will learn about different types of sequences.

### Directions

Simple Sequences
A sequence is a set of numbers that follows a mathematical rule and a specific order. This is a simple sequence:
(1, 2, 3, 4, 5, 6, 7, 8, . . .)
Odd numbers create a sequence following a specific arrangement:
(1, 3, 5, 7, 9, 11, 13, . . .)
Sequences can be used with all four operations and with combinations of operations.
Multiplication Sequences
Here is a multiplication sequence called the doubling sequence:
(1, 2, 4, 8, 16, . . .)
Multiplication sequences are also called geometric progressions. The multiplication sequence below involves square numbers. It is the square of each of the counting numbers.
(1, 4, 9, 16, 25, 36, . . .)
Declining Sequences
Sequences with subtraction and division decline from higher to lower numbers.
(28, 25, 22, 19, 16, 13, . . .) -- The rule is: (n - 3).
(88, 44, 22, 11, . . .) -- The rule is: (n ÷ 2).
Harder Sequences
Some sequences use two operations like this one -- (5, 11, 23, 47, 95, . . .)
The operations are multiply by 2 and add 1. The rule can be written this way: (n x 2) + 1
This sequence also employs two operations -- (5, 9, 17, 33, 65, . . .)
The operations are multiply by 2 and subtract 1. The rule can be written this way: (n x 2) - 1
Fibonacci Sequences
The most famous sequence is called the Fibonacci sequence. The first two numbers are 1. Every number after that is the sum of the preceding two numbers. Sequences can be designed to follow this Fibonacci pattern.
(1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89)

### Resources

• Copies of activity sheets for students