Sequence and difference sequence
Author: Andreas Bauer
Date: 19. November 2010

A quadratic sequence (red) and its difference sequence (green). Note how they behave exactly like a function and its derivative when varying the sliders.

n

a(n)

D(n)

p = 0.1 (slider from -1 to 1, step 0.1)
q = 0 (slider from -5 to 5, step 0.1)
t = 1 (slider from -5 to 5, step 0.1)
f(x) = p * x^(2) + q * x + t
Liste1 = Sequence((n, f(n)), n, 0, 100)
Liste2 = Sequence((n, f(n + 1) - f(n)), n, 0, 100)
Text2: "D_a(n) = " + (2 * p) + "n + " + q
A2 = 0
A3 = 1
B2: f(A2)
A4: 2 * A3 - A2
A5: 2 * A4 - A3
A6: 2 * A5 - A4
A7: 2 * A6 - A5
A8: 2 * A7 - A6
A9: 2 * A8 - A7
A10: 2 * A9 - A8
A11: 2 * A10 - A9
A12: 2 * A11 - A10
A13: 2 * A12 - A11
A14: 2 * A13 - A12
A15: 2 * A14 - A13
A16: 2 * A15 - A14
A17: 2 * A16 - A15
A18: 2 * A17 - A16
A19: 2 * A18 - A17
A20: 2 * A19 - A18
A21: 2 * A20 - A19
A22: 2 * A21 - A20
A23: 2 * A22 - A21
A24: 2 * A23 - A22
A25: 2 * A24 - A23
A26: 2 * A25 - A24
A27: 2 * A26 - A25
A28: 2 * A27 - A26
A29: 2 * A28 - A27
A30: 2 * A29 - A28
B3: f(A3)
B4: f(A4)
B5: f(A5)
B6: f(A6)
B7: f(A7)
B8: f(A8)
B9: f(A9)
B10: f(A10)
B11: f(A11)
B12: f(A12)
B13: f(A13)
B14: f(A14)
B15: f(A15)
B16: f(A16)
B17: f(A17)
B18: f(A18)
B19: f(A19)
B20: f(A20)
B21: f(A21)
B22: f(A22)
B23: f(A23)
B24: f(A24)
B25: f(A25)
B26: f(A26)
B27: f(A27)
B28: f(A28)
B29: f(A29)
B30: f(A30)
B31 = 0
C2: B3 - B2
C3: B4 - B3
C4: B5 - B4
C5: B6 - B5
C6: B7 - B6
C7: B8 - B7
C8: B9 - B8
C9: B10 - B9
C10: B11 - B10
C11: B12 - B11
C12: B13 - B12
C13: B14 - B13
C14: B15 - B14
C15: B16 - B15
C16: B17 - B16
C17: B18 - B17
C18: B19 - B18
C19: B20 - B19
C20: B21 - B20
C21: B22 - B21
C22: B23 - B22
C23: B24 - B23
C24: B25 - B24
C25: B26 - B25
C26: B27 - B26
C27: B28 - B27
C28: B29 - B28
C29: B30 - B29
Text1: "a(n) = " + (LaTeX[p]) + "n² + " + (LaTeX[q]) + "n + " + (LaTeX[t]) + ""