Arithmetic Sequence

Discussion Questions:

1. What do you notice about the two sequences? Compare the two.

2. What is the rule that creates the next term?

3. What do you call these type of sequences?

​Bellwork

​What are the next three terms in the sequences of numbers below?

a. 3, 6, 9, 12, 15, 18, 21

b. 10, 5, 0, -5, -10, -15

​An arithmetic sequence is a sequence in which each term after the first is found by adding a constant (common difference) to the previous term.

1, 2, 3, 4, 5, ... (common difference is 1)
2, 4, 6, 8, 10, ... (common difference is 2)
5, 10, 15, 20, 25, ... (common difference is 5)
3, 7, 11, 15, 19, ... (common difference is 4) 
10, 8, 6, 4, 2, ... (common difference is -2)



Key points about arithmetic sequences: 

• Each term is found by adding a constant value (called the common difference) to the previous term.

• You can identify an arithmetic sequence by checking if the difference between any two consecutive terms is always the same.

In the sequence 5, 8, 11, 14, ..., what is the common difference? Solve for the 10th term using the formula.



I do

Where:
a_n = the nth term
a₁ = the first term
d = common difference
n = term number

​a_n = a₁ + (n-1)d

​Find the 7th term in the sequence where the first term is a₁=2 and the common difference is d=4.






We do (Two ways to solve)

​Group A - Complete scaffolded worksheets
Group B - Work on a worksheet involving the general formula for arithmetic sequence
Group C - Create and solve real-world problems involving arithmetic sequence

You do