th
Students will be able to effectively represent everyday problem situations by writing an expression or equation and vice versa. Students will be able to generate different representations of data given one representation. Students will use the common difference in an arithmetic sequence to generate the expression relating the value of the term and its position in the sequence.
EXPRESSION – a mathematical representation consisting of symbols, operations and/or variables.
Ex: 2x-3
EQUATIONS – a mathematical sentence made up of more than one expression connected by an equal sign.
Ex: 3x+7=x-3
TERMS – all the parts of expressions or equations. In an arithmetic sequence, terms are the values (or numbers) in the list.
ARITHMETIC SEQUENCES – a list of numbers that have a common difference (constant rate of change) between each pair of consecutive numbers.
The numbers are called the terms in the sequence and the order that they are written gives the term’s position, n. Also called nth term.
Ex: 4, 8, 12, 16, …. (this means it keeps going)
The first number is 4 so its in the 1 st position (or n=1)
The second number is 8 so its in the 2
The third number is 12 so its in the 3 rd nd position (or n=2)
position (or n=3)
FIND THE RULE OF THE SEQUENCE - (this is the expression that relates the term to its position)
1.
you must first figure out what the common difference is
2.
multiply the common difference times n
3.
test the rule with n=1 to see if it equals the 1 see if it equals the 2 nd st term, n=2 to term.
4.
if yes to all three, then your rule is the common difference times n
term, n=3 to see if it equals the 3 rd

if no, then you must figure out what you need to add OR subtract from the product to get the 1 st term, 2 nd term, etc…
Ex1: 4, 8, 12, 16, … Question: What is the rule?
4 4 4 , the common difference is 4 because
8-4=4, 12-8=4, 16-12=4
***so we start with 4n as the rule
substitute 1 for n and see if = 1 st term…then substitute 2 for n and see if = 2 nd term, then substitute 3 for n to see if = 3 rd term….4(1)=4
4(2)=8
4(3)=12
YES…4, 8, 12 are the first three numbers in the sequence, so the rule is 4n for this sequence
Ex 2: Question: What is the rule for the sequence:
Position (n) 1 2 3 4
Term 5 13 21 29
The sequence is organized in a table, but it’s the same thing as writing:
5, 13, 21, 29, …
the common difference is 8 so we write 8n
8(1) = 8 – 3 = 5
8(2) = 16 – 3 = 13
8(3) = 24 – 3 = 21
The rule is: 8n – 3
So you must subtract 3 from the rule in order for it to work for all the terms.
Ex3: Question: Using the rule, 8n – 3, find the 30 th sequence.
term in the
If you need to find the 30 th term, that means you have to find term in the 30
8(30) – 3
240 – 3 th position. This means n = 30. So substitute 30 for n in the rule and it will equal to the 30 th term.

237 is the 30 th term