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Maths Gcse Edexcel Higher

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  1. Scatter-Graphs-And-Correlation Edexcel Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Edexcel Higher
    4 主题
  3. Histograms Edexcel Higher
    3 主题
  4. Statistical-Diagrams Edexcel Higher
    7 主题
  5. Averages-Ranges-And-Data Edexcel Higher
    8 主题
  6. Combined-And-Conditional-Probability Edexcel Higher
    3 主题
  7. Tree-Diagrams Edexcel Higher
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  8. Simple-Probability-Diagrams Edexcel Higher
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  9. Transformations Edexcel Higher
    5 主题
  10. Vectors Edexcel Higher
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  11. 3D-Pythagoras-And-Trigonometry Edexcel Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Edexcel Higher
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  13. Pythagoras-And-Trigonometry Edexcel Higher
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  14. Area-And-Volume-Of-Similar-Shapes Edexcel Higher
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  15. Congruence-Similarity-And-Geometrical-Proof Edexcel Higher
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  16. Volume-And-Surface-Area Edexcel Higher
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  17. Circles-Arcs-And-Sectors Edexcel Higher
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  18. Area-And-Perimeter Edexcel Higher
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  19. Circle-Theorems Edexcel Higher
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  20. Bearings-Scale-Drawing-Constructions-And-Loci Edexcel Higher
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  21. Angles-In-Polygons-And-Parallel-Lines Edexcel Higher
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  22. Symmetry-And-Shapes Edexcel Higher
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  23. Exchange-Rates-And-Best-Buys Edexcel Higher
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  24. Standard-And-Compound-Units Edexcel Higher
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  25. Direct-And-Inverse-Proportion Edexcel Higher
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  26. Problem-Solving-With-Ratios Edexcel Higher
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  27. Ratios Edexcel Higher
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  28. Sequences Edexcel Higher
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  29. Transformations-Of-Graphs Edexcel Higher
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  30. Graphing-Inequalities Edexcel Higher
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  31. Solving-Inequalities Edexcel Higher
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  32. Real-Life-Graphs Edexcel Higher
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  33. Estimating-Gradients-And-Areas-Under-Graphs Edexcel Higher
    2 主题
  34. Equation-Of-A-Circle Edexcel Higher
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  35. Graphs-Of-Functions Edexcel Higher
    6 主题
  36. Linear-Graphs Edexcel Higher
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  37. Coordinate-Geometry Edexcel Higher
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  38. Functions Edexcel Higher
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  39. Forming-And-Solving-Equations Edexcel Higher
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  40. Iteration Edexcel Higher
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  41. Simultaneous-Equations Edexcel Higher
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  42. Quadratic-Equations Edexcel Higher
    4 主题
  43. Linear-Equations Edexcel Higher
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  44. Algebraic-Proof Edexcel Higher
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  45. Rearranging-Formulas Edexcel Higher
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  46. Algebraic-Fractions Edexcel Higher
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  47. Completing-The-Square Edexcel Higher
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  48. Factorising Edexcel Higher
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  49. Expanding-Brackets Edexcel Higher
    3 主题
  50. Algebraic-Roots-And-Indices Edexcel Higher
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  51. Introduction Edexcel Higher
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  52. Using-A-Calculator Edexcel Higher
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  53. Surds Edexcel Higher
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  54. Rounding-Estimation-And-Bounds Edexcel Higher
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  55. Fractions-Decimals-And-Percentages Edexcel Higher
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  56. Simple-And-Compound-Interest-Growth-And-Decay Edexcel Higher
    4 主题
  57. Percentages Edexcel Higher
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  58. Fractions Edexcel Higher
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  59. Powers-Roots-And-Standard-Form Edexcel Higher
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  60. Prime-Factors-Hcf-And-Lcm Edexcel Higher
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  61. Number-Operations Edexcel Higher
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Exam code:1MA1

Quadratic sequences

What is a quadratic sequence?

  • A quadratic sequence has an n th term formula that involves n2

  • The second differences are constant (the same)

    • These are the differences between the first differences

    • For example, 3, 9, 19, 33, 51, …
      1st Differences: 6, 10, 14, 18, …

      2nd Differences: 4, 4, 4, …

  • The sequence with the n th term formula n2 are the square numbers 

    • 1, 4, 9, 16, 25, 36, 49, …

      • From 12, 22, 32, 42, …

How do I find the nth term formula for any quadratic sequence?

  • STEP 1
    Work out the sequences of first and second differences

    • e.g. for the sequence 1, 10, 23, 40, 61

sequence

1

10

23

40

61

first difference

+9

+13

+17

+21

second difference

+4

+4

+4

  • STEP 2
    Divide the second difference by 2 to find the coefficient of n2

    • e.g. a = 4 ÷ 2 = 2

  • STEP 3
    Write out the first three or four terms of an2 and subtract the terms from the corresponding terms of the given sequence

    • e.g. for the sequence 1, 10, 23, 40, 61

sequence

1

10

23

40

2n2

2

8

18

32

difference

-1

2

5

8

  • STEP 4
    Work out the nth term of these differences to find the bn + c part of the formula

    • e.g. the nth term of -1, 2, 5, 8, … is bn + c = 3n − 4

  • STEP 5
    Find an2 + bn + c by adding together this linear nth term to an2 term

    • e.g. an2 + bn + c = 2n2 + 3n − 4

Examiner Tips and Tricks

  • You must learn the square numbers from 12 to 152

Worked Example

For the sequence 5, 7, 11, 17, 25, ….

(a) Find a formula for the nth term.
Start by finding the first and second differences

Sequence: 5, 7, 11, 17, 25

First differences: 2, 4, 6, 8, …

Second difference: 2, 2, 2, …

Hence 

a = 2 ÷ 2 = 1

Now write down an2 (just n2 in this case as a = 1) and subtract the terms from the original sequence

sequence: 5, 7, 11, 17, …

an2. : 1, 4, 9, 16, …

 difference: 4, 3, 2, 1, …

Work out the nth term of these differences to give you bn + c

bn + c = −n + 5

Add an2 and bn + c together to give you the nth term of the sequence

nth term = n2 − n + 5

(b) Hence find the 20th term of the sequence.

Substitute n = 20 into n2 − n + 5

(20)2 − 20 + 5 = 400 − 15 

20th term = 385

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