ALGEBRA · SEQUENCES · INVESTIGATION 13
Arithmetic Progression Explorer
Investigate common difference, nth term and partial sums in arithmetic progressions.
Interactive mathematical workspace
Live simulationThe model updates as you adjust the apparatus controls. Values are simulated mathematical outputs, not physical measurements.
Primary result—
Secondary result—
Relationship—
Check—
Adjust a control to begin the investigation.
Learning objective
To investigate Arithmetic Progression Explorer using a dynamic mathematical model and justify a conclusion from recorded values.
Mathematical principle
aₙ = a + (n−1)d · Sₙ = n/2[2a+(n−1)d]
Procedure
1
Enter student details and note the initial settings.
2
Change one independent variable while keeping the others fixed.
3
Observe the visual model and note the calculated values.
4
Repeat with at least three different settings and record the readings.
5
Use the pattern in your observations to write a mathematical conclusion.
Variables
Independent: the control being changed. Dependent: calculated result. Controlled: other settings held constant.
Guided investigation: Change a and d, then inspect the sequence and cumulative sum.
Common errors to avoid
- Changing several variables simultaneously.
- Recording rounded values before completing calculations.
- Confusing linear, square and cubic units.
- Writing a conclusion that is not supported by observations.
Live mathematical analysis
aₙ = a + (n−1)d · Sₙ = n/2[2a+(n−1)d]
The working will appear here.
Observation table
| Trial | Settings | Result 1 | Result 2 |
|---|---|---|---|
| Run and record trials to populate this table. | |||
Compare the readings and identify the pattern.
Digital practical notebook
Recorded trials
| # | Settings | Result 1 | Result 2 | Time |
|---|
Knowledge check
Select the best answer. Feedback is provided after checking.
Assessment score0 / 5
Investigation challenge
For a=3, d=2, find the 8th term and sum of 8 terms.