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Arithmetic Sequence Sum

Arithmetic Sequence Sum
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2015-05-09 06:13
FunctionSequenceCoordinate Geometry
This example demonstrates the dynamic visualization of the sum formula for arithmetic sequences. It involves core math concepts like arithmetic sequences, sum formulas, and coordinate geometry. Construction highlights include using GeoGebra's Sequence and Text commands, with objects like n, d, a1, list1, list2, text1, TEXT1, TEXT2, text5, text6. Suitable for high school mathematics teaching to understand the application and derivation of arithmetic sequence sum formulas.

GeoGebra Commands & Parameters

  1. Sequence(Polygon[(0, (-k)), (0, (-k) - 1), (a1 + (k * d), (-k) - 1), (a1 + (k * d), (-k))], k, 0, n - 1) → list1
  2. Sequence(Polygon[(a1 + (k * d), (-k)), (a1 + (k * d), (-k) - 1), ((2 * a1) + (n * d) - d, (-k) - 1), ((2 * a1) + (n * d) - d, (-k))], k, 0, n - 1) → list2
  3. Text(("n = " * n), ((-1.3), ((-n)) / 2)) → text1
  4. Text(("a1 = " * a1), (a1 / 2 - 0.1, 0.4)) → TEXT1
  5. Text(((("a" * n) * " = ") * (a1 + ((n - 1) * d))), (((3 * a1) + ((n - 1) * d)) / 2 - 0.1, 0.4)) → TEXT2
  6. Text(("שטח מלבן = " * (((2 * n) * a1) + (((n - 1) * d) * n))), (a1 / 2 - 0.1, 4)) → text5
  7. Text(((((("( " * a1) * " + ") * (a1 + ((n - 1) * d))) * " ) * ") * n), (a1 / 2 - 0.1, 5.1)) → text6