One-to-One Correspondence
What does it mean for an arithmetic sequence to have one-to-one correspondence between positions and terms?
It means that each position in the sequence has exactly one matching number (term).
Describe what the graph of an arithmetic sequence looks like.
The graph is a straight line that goes up or down.
Write a rule for the sequence 3, 6, 9.
The rule is n = 3n (multiply the position by 3).
What is the missing term in the sequence: 3, __, 9, 12?
The missing term is 6.
If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the third term?
The third term is 11 (because 5 + 3 + 3 = 11).
If you plot the terms of the sequence 1, 4, 7 on a coordinate grid, what type of line will you draw?
The points show the position number and the term value (like (1,1), (2,4), (3,7)).
What operation can be used to find the next term in the arithmetic sequence 10, 15, 20?
Addition (you add 5 each time).
If the 2nd term is 10 and the 4th term is 16, what is the missing 3rd term?
The missing term is 13.
Complete the table: Position: 1, 2, 3; Term: 5, , .
1, 2, 3 → Term: 5, 8, 11
What do the points on the graph of an arithmetic sequence represent?
The slope will be 2 because the line moves up by 2 every step.
If the first term is 8 and the common difference is 2, what is the rule for finding any term?
n = 2n + 6 (multiply the position by 2 and add 6).
In the sequence 4, _, 16, 20, what is the missing term?
The missing term is 12.
How would you represent the correspondence between the position and the term of the sequence 2, 5, 8, 11, in a table?
Compare your answers.
If the common difference of an arithmetic sequence is 2, how will the slope of the graph be affected?
The slope will be 2 because the line moves up by 2 every step.
Create a rule for finding the (n)th term of the sequence 5, 10, 15.
n = 5n (multiply the position by 5).
Find the missing term in the sequence where the first term is 2 and the common difference is 3: 2, 5, _, 11.
The missing term is 8.
If the position is represented by (n), write a rule using one operation for the sequence 4, 7, 10, 13.
The rule is n = 3n + 1 (multiply the position by 3, then add 1).
How can you tell if a sequence is arithmetic just by looking at its graph?
If the points form a straight line, it's an arithmetic sequence.
How can you express the rule for an arithmetic sequence in words?
You can say, "Start at the first term and keep adding the common difference."
If the position is 5 and the term is 30 in the sequence 3, 6, 9, …, what is the missing term for position 4?
The missing term is 27.