Sequence and difference sequence
Author: Andreas Bauer
Date: 21. Juli 2011

To a given sequence a(n) = n² (green), we want to find its difference sequence Da(n) := a(n+1) - a(n).

Use the spreadsheet to create a cell formula which calculates the difference sequence's values in the cells C3 to C30. 

Plot the difference sequence with the button in the upper left part of the graphics window. Describe its graph. How is the graph's slope represented in the spreadsheet?

n

a(n)

Da(n)

Plot Da(n)

k = 1 (slider from 0 to 5, step 0.1)
A2 = 1
A3 = 2
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
A31: 2 * A30 - A29
f(x) = k * x^(2)
B2: f(A2)
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: f(A31)
Liste1: {(A2, B2), (A3, B3), (A4, B4), (A5, B5), (A6, B6), (A7, B7), (A8, B8), (A9, B9), (A10, B10), (A11, B11)}
C2 = 3
Q_1: (A2, C2)
Text1: "a(n) = " + (LaTeX[k]) + " \cdot n^2"
anchor = Element(Liste1, 6)