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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
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  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
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  3. Histograms Aqa Higher
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  4. Statistical-Diagrams Aqa Higher
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  5. Averages-Ranges-And-Data Aqa Higher
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  6. Combined-And-Conditional-Probability Aqa Higher
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  7. Tree-Diagrams Aqa Higher
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  8. Simple-Probability-Diagrams Aqa Higher
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  9. Transformations Aqa Higher
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  10. Vectors Aqa Higher
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  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
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  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
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  13. Pythagoras-And-Trigonometry Aqa Higher
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  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
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  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
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  16. Volume-And-Surface-Area Aqa Higher
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  17. Circles-Arcs-And-Sectors Aqa Higher
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  18. Area-And-Perimeter Aqa Higher
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  19. Circle-Theorems Aqa Higher
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  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
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  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
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  22. Symmetry-And-Shapes Aqa Higher
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  23. Exchange-Rates-And-Best-Buys Aqa Higher
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  24. Standard-And-Compound-Units Aqa Higher
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  25. Direct-And-Inverse-Proportion Aqa Higher
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  26. Problem-Solving-With-Ratios Aqa Higher
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  27. Ratios Aqa Higher
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  28. Sequences Aqa Higher
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  29. Transformations-Of-Graphs Aqa Higher
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  30. Graphing-Inequalities Aqa Higher
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  31. Solving-Inequalities Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
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  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
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  34. Equation-Of-A-Circle Aqa Higher
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  35. Functions Aqa Higher
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  36. Forming-And-Solving-Equations Aqa Higher
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  37. Graphs-Of-Functions Aqa Higher
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  38. Linear-Graphs Aqa Higher
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  39. Coordinate-Geometry Aqa Higher
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  40. Iteration Aqa Higher
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  41. Simultaneous-Equations Aqa Higher
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  42. Quadratic-Equations Aqa Higher
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  43. Linear-Equations Aqa Higher
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  44. Algebraic-Proof Aqa Higher
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  45. Rearranging-Formulas Aqa Higher
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  46. Algebraic-Fractions Aqa Higher
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  47. Completing-The-Square Aqa Higher
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  48. Factorising Aqa Higher
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  49. Expanding-Brackets Aqa Higher
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  50. Algebraic-Roots-And-Indices Aqa Higher
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  51. Using-A-Calculator Aqa Higher
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  52. Surds Aqa Higher
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  53. Rounding-Estimation-And-Bounds Aqa Higher
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  54. Fractions-Decimals-And-Percentages Aqa Higher
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  55. Introduction Aqa Higher
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  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
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  57. Percentages Aqa Higher
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  58. Fractions Aqa Higher
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  59. Powers-Roots-And-Standard-Form Aqa Higher
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  61. Number-Operations Aqa Higher
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Exam code:8300

Introduction to sequences

What are sequences?

  • A sequence is an ordered set of numbers that follow a rule

    • For example 3, 6, 9, 12…

      • The rule is to add 3 each time

  • Each number in a sequence is called a term

  • The location of a term within a sequence is called its position

    • The letter n  is used for position

      • n = 1 refers to the 1st term

      • n = 2 refers to the 2nd term

      • If you do not know its position, you can say the n th term

  • Another way to show the position of a term is using subscripts

    • A general sequence is given by a1, a2, a3, …

      • a1 represents the 1st term

      • a2 represents the 2nd term

      • an represents the nth term

A sequence of numbers

How do I write out a sequence using a term-to-term rule?

  • Term-to-term rules tell you how to get the next term from the term you are on

    • It is what you do each time

    • For example, starting on 4, add 10 each time

      • 4, 14, 24, 34, …

How do I write out a sequence using a position-to-term rule?

  • A position-to-term rule is an algebraic expression in n that lets you find any term in the sequence

    • This is also called the n th term formula

  • You need to know what position in the sequence you are looking for

    • To get the 1st term, substitute in n = 1

    • To get the 2nd term, substitute in n  = 2

  • You can jump straight to the 100th term by substituting in n = 100

    • You do not need to find all 99 previous terms

  • For example, the n th term is 8n + 2

    • The 1st term is 8×1 + 2 = 10

    • The 2nd term is 8×2 + 2 = 18

    • The 100th term is 8×100 + 2 = 802

How do I know if a value belongs to a sequence?

  • If you know the n th term formula, set the value equal to the formula

    • This creates an equation to solve for n

  • For example, a sequence has the n th term formula 8n  + 2

    • Is 98 in the sequence?
      table row cell 8 n plus 2 end cell equals 98 row cell 8 n end cell equals 96 row n equals cell 96 over 8 end cell row n equals 12 end table

      • It is in the sequence, it is the 12th term

    • Is 124 in the sequence?
      table row cell 8 n plus 2 end cell equals 124 row cell 8 n end cell equals 122 row n equals cell 122 over 8 end cell row n equals cell 15.25 end cell end table

      • n is not a whole number, so it is not in the sequence

Examiner Tips and Tricks

  • In the exam, it helps to write the position number (the value of n) above each term in the sequence.

Worked Example

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