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Sum of the First n Terms of an Arithmetic Sequence

Sum of the First n Terms of an Arithmetic Sequence
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2019-04-10 18:27
VectorSequenceCoordinate Geometry
This example demonstrates the sum of the first n terms of an arithmetic sequence. Key mathematical concepts include arithmetic sequences and summation formulas. Using GeoGebra commands such as Sequence, Vector, and Translate, the generation process of the sequence can be dynamically displayed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(j, (-i)), j, 1, i], i, 1, 10) → l1
  2. Sequence(Sequence[(j, (-i)), j, 1, 3], i, 3, 20, 2) → l2
  3. Sequence(Sequence[(j, (-i)), j, 4, i], i, 3, 20, 2) → l3
  4. Sequence((0, k), k, -3, -11, -1) → l5
  5. Sequence((0, k), k, -3, -19, -2) → l4
  6. Sequence(Vector[Element[l4, k], Element[l5, k]], k, 1, 9) → l6
  7. Sequence(Translate[Element[l2, k], Vector[Element[l6, k]]], k, 1, 9) → l7
  8. Sequence(Translate[Element[l3, k], Vector[Element[l6, k]]], k, 1, 9) → l8
  9. Vector(A, B) → u
  10. If(0 ≤ a < 1, Vector[Dilate[u, a, A]], Vector[If[a ≥ 1, u]]) → v
  11. Translate(l7, v) → l9
  12. Translate(l8, v) → l10
  13. If(1 ≤ a < 2, Rotate[l9, β, C], If[a ≥ 2, Rotate[l9, α, C]]) → l11
  14. If(1 ≤ a < 2, Rotate[l10, β, C], If[a ≥ 2, Rotate[l10, α, C]]) → l12
  15. Vector(D, E) → w
  16. If(2 ≤ a < 3, Vector[Dilate[w, a - 2, D]], Vector[If[a ≥ 3, w]]) → b
  17. Translate(l11, b) → l13
  18. Translate(l12, b) → l14
  19. Segment(F, G) → f
  20. Segment(H, I) → g
  21. Segment(J, K) → h
  22. Segment(L, M) → i
  23. Segment(N, O) → j
  24. Sequence((-1, k), k, -3, -11, -1) → l17
  25. Sequence(Text[Element[l15, k], Element[l17, k]], k, 1, 9) → l16
  26. Segment(P, Q) → k
  27. Segment(R, S) → l
  28. Sequence((24, k), k, -3, -11, -1) → l18
  29. Sequence(Text[Element[l15, k], Element[l18, 10 - k]], k, 1, 9) → l19
  30. PolyLine(T, U, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, V, W, Z, A_1, B_1, C_1, D_1, E_1) → m
  31. Polygon(N_1, O_1, Q_1, P_1) → q1, n_1, o_1, q_1, p_1
  32. Segment(R_1, S_1) → n

AI Drawing Prompt Reference

Draw a diagram illustrating the sum of the first n terms of an arithmetic sequence, featuring multiple sequences of points connected by vectors, with translations and rotations to show the generation process. Include several line segments and text labels indicating the terms and sums, constructing the complex structure from simple sequences through vector operations and transformations.
The prompt above was compiled from the original drawing commands and is for reference only.