Arithmetic Patterns Simulation

Pattern evidenceLive observation

Build a sequence and test the change from one term to the next.

Position1

Term value3

Difference+4

Rule3 + 4(n−1)

Arithmetic Pattern WorkshopPaused

ModeStudent

How does an arithmetic pattern grow?

The same number is added or subtracted every time. The workshop links term position, term value, equal jumps, and a growing visual pattern.

Choose a first term.
Apply one common difference.
Predict any term from its position.

Rule machine

Sound

First term3

Common difference+4

Number of terms8

Selected position1

Representation

Simulation speed1×

Current relationship

Previous term—

Current term3

Next term7

Pattern typeIncreasing

View and term focus

Drag to pan, use the wheel or buttons to zoom, and tap any number tile to inspect it.

Position-value history

Teacher demonstrations

Guided visual lecture

Chapter 1 of 80%

Ready. Clear embedded audio is synchronized to every label, jump, and visual change.

Language

Narrator

Playback speed1×

External recording: share this browser tab with tab audio enabled. Embedded audio is louder and recordable; no microphone is used.

1. What is an arithmetic pattern?

Watch: Number tiles pass through one consistent rule machine.

Chapters

Arithmetic sequence formulas

Common difference: d = a_n+1 − a_n

Term at position n: a_n = a₁ + (n − 1)d

Sum of the first n terms: S_n = n[2a₁ + (n − 1)d] ÷ 2

The same difference makes the position-value graph a straight line. Its vertical change per step is d.

Learning objectives

Recognize a constant difference between consecutive terms.
Classify increasing, decreasing, and constant patterns.
Use position to calculate any term.
Connect number, dot, staircase, and graph representations.

Suggested investigations

Set d to zero and explain the horizontal graph.
Use a negative difference and find when values cross zero.
Compare even and odd patterns that share d = 2.
Predict term 12 before revealing it.

Questions for exploration

How does changing a₁ move the graph?
How does changing d alter the staircase?
Can two patterns share a difference but have different terms?

Teacher whiteboard

Use a finger, stylus, mouse, Android device, or smart board. Ten full-size pages keep their own drawings.

Pen color

Line width4

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Knowledge check

Seven questions0 / 7

Choose an answer for instant feedback.