Learning objectives
Recall the slope-intercept form of a linear function:
Similarly, an arithmetic sequence is represented in explicit notation by the formula:
The domain of any arithmetic sequence is a subset of the integers. The domain can begin from any non-negative integer but will most often begin at 0 or 1.
We can also utilize point-slope form to help us write arithmetic sequences.
For an arithmetic sequence where a term and the common difference are known we can use a similar formula:
Arithmetic sequences are linear functions because both have a constant rate of change (slope or common difference) and an inital value (the first term or y-intercept).
Mandy has already folded 4 shirts before her shift officially begins at the clothing store. Additional information about the number of shirts she has folded at various times during her shift is given in the table.
Time (minutes) | 0 | 15 | 30 | 45 | 60 |
---|---|---|---|---|---|
Shirts folded | 4 | 19 | 34 | 49 | 64 |
State whether Mandy's number of shirts folded represent an arithmetic sequence.
Determine the linear function that represents the number of shirts Mandy has folded, S(t), as a function of time t (in minutes).
Calculate the number of shirts Mandy will have folded after 90 minutes.
Mandy's shirt folding business is growing. In 2023, she folded approximately 2,000 shirts each month. Between 2023 and 2028, the number of shirts she folded increased at approximately 3.5\% per year. According to this estimate, how many shirts did Mandy fold per month in 2025?
What is the ratio of shirt folding from 2025 compared to 2023?
An arithmetic sequence is a linear function because it has a constant rate of change.
When the first term and common difference are known:
When any term and the common difference are known: