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Patterns and sequences

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

A pattern of tiles hides a sequence of numbers (die Zahlenfolge). With a term you can quickly calculate big figures too.
📄 Open worksheet (PDF, German)

The video

In the video we continue a tile pattern and find the term \(2n + 1\).

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:20 The sequence
  3. 0:37 A term for the pattern
  4. 1:02 Careful, mistake!
  5. 1:30 Try it yourself

The most important points

Figure \(1\) has \(3\) tiles, figure \(2\) has \(5\), figure \(3\) has \(7\). With each figure \(2\) are added.

The tile pattern.
The tile pattern.

Sequence

\(3, 5, 7, 9, \dots\): from number to number, \(2\) are always added. It goes on: \(11, 13, 15\).

Always +2.
Always \(+2\).

Term

Figure \(n\) has \(n\) tiles on top and \(n + 1\) below: together \(2n + 1\). Figure \(10\): \(2 \cdot 10 + 1 = 21\).

n on top, n + 1 below.
\(n\) on top, \(n + 1\) below.

Careful: figure \(10\) does not have \(10 \cdot 3 = 30\) tiles. Only \(2\) are added each time.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/4
The worksheet – Page 2
Page 2/4
The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Sequence \(4, 7, 10, 13, \dots\): a) What are the next two numbers? b) Find a term for the \(n\)th number. c) What is the \(20\)th number?

Show solution

Always \(+3\): a) \(16, 19\) b) \(3n + 1\) c) \(3 \cdot 20 + 1 = 61\).

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Muster und Zahlenfolgen (fortsetzen, Term für die n-te Figur aufstellen). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.