 ## Sequences and Exponents

Mathematics, Operations (+, -, x, /, etc.), Problem Solving

### Objective

Students practice multiplication sequences and multiplying with exponents.

### Directions

Facts to Know
Sequences
A sequence is a set of numbers which follows a mathematical rule.
Sequences can be used with all four operations and with combinations of operations.
This is a simple sequence:
1, 2, 3, 4, 5, 6, 7, 8, ...
Here is a multiplication sequence called the doubling sequence.
1, 2, 4, 8, 16, ...
Some sequences use two operations like this one:
4, 9, 19, 39, 79, ...
The operations are multiply by 2 and add 1.
The rule can be written this way: (a x 2) + 1.
Multiplication sequences are also called geometric progressions.
Exponents
When a number is to be multiplied by itself, it can be written as an exponent.
The exponent is the small raised number which tells how many times to multiply the base number by itself.
Sample A
52 means multiply 5 times 5.
5 is the base number.
The raised number 2 is the exponent. It also indicates that 5 is being raised to the second power.
Sample B
53 = 5 x 5 x 5
This indicates that 5 is to be multiplied by itself, and the answer (25) is to be multiplied again by 5.
5 x 5 = 25
25 x 5 = 125
53 = 125
Sample C
34 = 3 x 3 x 3 x 3
This exponent (or the raised number) indicates that 3 is to be multiplied by 3.
The answer (9) is to be multiplied by 3 again.
The answer (27) is to be multiplied by 3 again.
3 x 3 = 9
9 x 3 = 27
27 x 3 = 81
34 = 81

### Resources

• Multiplication Sequences, Multiplying with Exponents, and Multiplying with Higher-Power Exponents activity sheets
• pencils