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Representations of Sequences

Representations of Sequences
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2019-03-13 01:24
FunctionSequenceCalculus
This example demonstrates different representations of sequences. Key mathematical concepts include sequences and series. Using GeoGebra commands such as Sequence, Flatten, and Shuffle, the example constructs recursive formulas, general terms, and scatter plots. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(Polygon[{tableAnchor + (col1Width + col2Width + col3Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width + col4Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width + col4Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (col1Width + col2Width + col3Width, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol4
  2. Sequence(Polygon[{tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (col1Width + col2Width, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol3
  3. Sequence(Polygon[{tableAnchor + (col1Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (col1Width, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol2
  4. Flatten(Sequence[Sequence[(i, j), i, -8, -8 + (2 * (tileWidth + 1)), tileWidth + 1], j, 3, 3 - (2 * (tileHeight + 1)), (-tileHeight) - 1]) → fixedFrameAnchors
  5. Shuffle(fixedFrameAnchors) → shuffledFrameAnchors
  6. LaTeX(UnicodeToLetter[10003]) → cmark
  7. LaTeX(UnicodeToLetter[10007]) → xmark
  8. Sequence(Polygon[{tableAnchor + (0, 0 - (rowHeight * i)), tableAnchor + (col1Width, 0 - (rowHeight * i)), tableAnchor + (col1Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (0, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol1
  9. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  10. Text("Recursion Formula", tableAnchor + (0.5 + col1Width, ((-rowHeight)) / 2)) → col2Header
  11. Text("General Term", tableAnchor + (0.5 + col1Width + col2Width, ((-rowHeight)) / 2)) → col3Header
  12. Text("Discrete Function", tableAnchor + (0.5 + col1Width + col2Width + col3Width, ((-rowHeight)) / 2)) → col4Header
  13. Text("160, 156, 152, \ldots", tableAnchor + (0, (-rowHeight) - rowHeight / 3), true, true) → sequence1
  14. Text("160, 80, \tfrac{160}{3}, \ldots", tableAnchor + (0, ((-rowHeight) * 3) - rowHeight / 3), true, true) → sequence3
  15. Text("160, 152, 140, \ldots", tableAnchor + (0, ((-rowHeight) * 2) - rowHeight / 3), true, true) → sequence2
  16. Zip(Polygon[A, A + (tileWidth, 0), A + (tileWidth, (-tileHeight)), A + (0, (-tileHeight))], A, shuffledFrameAnchors) → frames
  17. Element(frames, 1) → frame1
  18. Element(frames, 2) → frame2
  19. Element(frames, 3) → frame3
  20. Element(frames, 4) → frame4
  21. Element(frames, 5) → frame5
  22. Element(frames, 6) → frame6
  23. Element(frames, 7) → frame7
  24. Element(frames, 8) → frame8
  25. Element(frames, 9) → frame9
  26. Element(cells, 1) → cell1
  27. Element(frames, activeTile) → highlightedTile
  28. Element(cells, 2) → cell2
  29. Element(cells, 3) → cell3
  30. Element(cells, 4) → cell4
  31. Element(cells, 5) → cell5
  32. Element(cells, 7) → cell7
  33. Element(cells, 8) → cell8
  34. Element(cells, 9) → cell9
  35. Element(cells, activeCell) → highlightedCell
  36. Element(tableCol1, 1) → col1HeaderCell
  37. Text("Sequence", tableAnchor + (0.5, ((-rowHeight)) / 2)) → col1Header
  38. Element(tableCol2, 1) → col2HeaderCell
  39. Element(tableCol3, 1) → col3HeaderCell
  40. Element(tableCol4, 1) → col4HeaderCell
  41. Element(cells, 6) → cell6
  42. Zip(A ≟ B, A, itemsInCells, B, 1…9) → cellsCorrect
  43. Zip(Text[If[A, cmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → cmarkList
  44. Zip(Text[If[¬A, xmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → xmarkList
  45. LaTeX("\text{You found three different algebraic representations for each sequence.}") → feedback

AI Drawing Prompt Reference

Draw multiple representations of sequences, including recursive formulas, general terms, and discrete functions. Start by drawing a table with four columns: recursive formulas, general terms, discrete functions, and sequences. Then input three sequences: 160, 156, 152, ...; 160, 80, 160/3, ...; 160, 152, 140, .... Next, draw nine blocks below the table to represent the terms of the sequences, and mark the current term with different colors. Finally, add titles above the table: recursive formulas, general terms, discrete functions, and sequences.
The prompt above was compiled from the original drawing commands and is for reference only.