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Arithmetic Sequence and Partial Sums

Arithmetic Sequence and Partial Sums
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2015-10-27 06:57
FunctionSequenceCoordinate GeometrySlider AnimationGraphing
This example demonstrates the graphical representation of an arithmetic sequence and its partial sums, illustrating the relationship between terms and their cumulative sums. Key math concepts include arithmetic sequences, partial sums, and the general term formula. The construction uses GeoGebra commands for objects A1-A20 and C1-C10, representing sequence terms and sum calculations. Suitable for high school mathematics education, helping students understand the connection between sequences, functions, and sum formulas.

GeoGebra Commands & Parameters

  1. Numeric A1(1.0)
  2. A1 + 1
  3. A2 + 1
  4. A3 + 1
  5. A4 + 1
  6. A5 + 1
  7. A6 + 1
  8. A7 + 1
  9. A8 + 1
  10. A9 + 1
  11. A10 + 1
  12. A11 + 1
  13. A12 + 1
  14. A13 + 1
  15. A14 + 1
  16. A15 + 1
  17. A16 + 1
  18. A17 + 1
  19. A18 + 1
  20. A19 + 1
  21. (0.5 * A1) - 2
  22. (0.500000000000002 * A2) - 2
  23. (0.500000000000002 * A3) - 2
  24. (0.500000000000002 * A4) - 2
  25. (0.500000000000002 * A5) - 2
  26. (0.500000000000002 * A6) - 2
  27. (0.500000000000002 * A7) - 2
  28. (0.500000000000002 * A8) - 2
  29. (0.500000000000002 * A9) - 2
  30. (0.500000000000002 * A10) - 2
  31. (0.500000000000002 * A11) - 2
  32. (0.500000000000002 * A12) - 2
  33. (0.500000000000002 * A13) - 2
  34. (0.500000000000002 * A14) - 2
  35. (0.500000000000002 * A15) - 2
  36. (0.500000000000002 * A16) - 2
  37. (0.500000000000002 * A17) - 2
  38. (0.500000000000002 * A18) - 2
  39. (0.500000000000002 * A19) - 2
  40. (0.500000000000002 * A20) - 2
  41. (A1, C1)
  42. (A2, C2)
  43. (A3, C3)
  44. (A4, C4)
  45. (A5, C5)
  46. (A6, C6)
  47. (A7, C7)
  48. (A8, C8)
  49. (A9, C9)
  50. (A10, C10)
  51. (A11, C11)
  52. (A12, C12)
  53. (A13, C13)
  54. (A14, C14)
  55. (A15, C15)
  56. (A16, C16)
  57. (A17, C17)
  58. (A18, C18)
  59. (A19, C19)
  60. (A20, C20)

AI Drawing Prompt Reference

Draw a graph to illustrate the relationship between an arithmetic sequence and its partial sums, using a slider to control the first term and common difference. Plot the first 20 terms of the sequence and the first 8 partial sums as points, then connect these points with lines to clearly show the growth trend of both the sequence and the partial sums.
The prompt above was compiled from the original drawing commands and is for reference only.