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Sequences (Cambridge (CIE) IGCSE Maths)

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  • What is a sequence?

    A sequence is an ordered set of (usually) numbers.

  • In the context of sequences, what is a term?

    A term is one of the numbers in a sequence.

  • In the context of sequences, what is n?

    n is the position of a term in a sequence.

    E.g. when n = 3, it is referring to the third term of the sequence.

  • True or False?

    For the first term, n = 0.

    False.

    For the first term, n = 1.

  • What is subscript notation for sequences?

    Subscript notation is used to talk about a particular term.

    For example

    • a subscript 1 is the 1st term

    • a subscript 7 is the 7th term

    • a subscript n is the nth term

  • What is a position-to-term rule?

    A position-to-term rule gives the nth term of a sequence as a formula in terms of n.

  • How would you find the first three terms of a sequence using a position-to-term rule?

    To find the first three terms of a sequence using a position-to-term rule, substitute n equals 1, n equals 2 and n equals 3 into the position-to-term formula.

  • What is a term-to-term rule?

    A term-to-term rule tells you how to find a term from the term before it.

    I.e., it gives the (n+1)th term in terms of the nth term.

  • What is an exponential sequence?

    An exponential sequence is a sequence where one term is multiplied by a common ratio to find the next term.

    E.g. the sequence: 3, 6, 12, 24, 48, ... is an exponential sequence with the common ratio 2.

    An exponential sequence is also known as a geometric sequence.

  • What is the position-to-term rule for an exponential sequence?

    The position-to-term rule (nth term rule) for an exponential sequence is a cross times r to the power of n minus 1 end exponent

    Where:

    • a is the first term

    • r is the common ratio

    • n is the position of the term in the sequence

  • How can a cubic sequence be identified from common differences?

    A cubic sequence can be identified by having a constant third difference.

    E.g. Consider the sequence: 1, 7, 17, 33, 57, ...
    The first differences are: 6, 10, 16, 24
    The second differences are: 4, 6, 8
    The third differences are: 2, 2
    The third differences are constant, therefore it is a cubic sequence.

  • What type of sequence is: 1, 3, 6, 10, 15, ... an example of?

    The sequence: 1, 3, 6, 10, 15, is the sequence of triangular numbers.

    (This is also an example of a quadratic sequence.)

  • True or False?

    If the common ratio in an exponential sequence is less than 1 but greater than 0, then it is an increasing sequence.

    False.

    If the common ratio in an exponential sequence is less than 1 but greater than 0, then it is a decreasing sequence.

    It is an increasing sequence if the common ratio is greater than 1.

  • What is a linear sequence?

    A linear sequence is a sequence of numbers that increase or decrease by the same amount from one term to the next.

    A linear sequence is often called an arithmetic sequence.

  • Define the common difference of a linear sequence.

    The common difference is the amount that a linear sequence increases or decreases by from one term to the next.

  • What is d the notation for in the context of linear sequences?

    d is the notation for the common difference of a linear sequence.

    E.g. for a sequence 3, 7, 11, 15, 19, ...
    d equals 4.

  • What is b the notation for in the context of linear sequences?

    b is the value before the first term (sometimes known as the zero term).

    E.g. for a sequence 3, 7, 11, 15, 19, ...
    The common difference is +4, so imagine going back from the first term by subtracting 4. So b equals negative 1.

  • What is the position-to-term formula for a linear sequence in terms of b, d and n?

    The position-to-term formula (also known as the nth term rule) for a linear sequence in terms of b, d and n is: n th space term equals d n plus b.

  • What is a quadratic sequence?

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

  • True or False?

    The first differences in a quadratic sequence are constant.

    False.

    The first differences in a quadratic sequence are not constant.

    The first differences form a linear sequence, which means that the second differences of a quadratic sequence are constant.

  • How do you find the nth term rule for a quadratic sequence?

    E.g. 3, 6, 11, 18, 27, ...

    To find the nth term rule for a quadratic sequence, compare the original sequence to the sequence of square numbers.

    E.g. each value in the sequence, 3, 6, 11, 18, 27, ... is 2 more than the sequence of square numbers, 1, 4, 9, 16, 25, ...

    So if the sequence of square numbers is n2, the original sequence is n2 + 2.

  • True or False?

    For a simple quadratic sequence of the form a n squared plus b, the value of a is twice the value of the second difference.

    False.

    For a simple quadratic sequence of the form a n squared plus b, the value of a is half the value of the second difference.

    E.g. for the quadratic sequence: 5, 11, 21, 35, 53, ...
    The first differences are: 6, 10, 14, 18
    The second differences are: 4, 4, 4
    Therefore, a equals 2.
    To find b, compare the original sequence to the sequence given by 2 n squared.
    The nth term rule for the original sequence is 2 n squared plus 3.

Previous:FunctionsNext:Proportion

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions Toolkit

    6. Topic 6

      Percentages Toolkit

    7. Topic 7

      Simple & Compound Interest, Growth & Decay

    8. Topic 8

      Surds

    9. Topic 9

      Working with FDP

    10. Topic 10

      Working with Ratios

    11. Topic 11

      Compound Measures (Speed, Density, Pressure)

    12. Topic 12

      Time, Currency & Conversions

    13. Topic 13

      Rounding, Estimation & Bounds

    14. Topic 14

      Using a Calculator

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding & Factorising Brackets

    4. Topic 4

      Linear Equations & Inequalities

    5. Topic 5

      Quadratic Equations

    6. Topic 6

      Rearranging Formulas

    7. Topic 7

      Simultaneous Equations

    8. Topic 8

      Algebraic Fractions

    9. Topic 9

      Forming & Solving Equations

    10. Topic 10

      Functions

    11. Topic 11

      Sequences

    12. Topic 12

      Proportion

    1. Topic 1

      Coordinate Geometry

    2. Topic 2

      Linear Graphs

    3. Topic 3

      Quadratic Graphs

    4. Topic 4

      Further Graphs & Tangents

    5. Topic 5

      Solving & Graphing Inequalities

    6. Topic 6

      Real-Life Graphs

    7. Topic 7

      Differentiation

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Constructions & Scale Drawings

    4. Topic 4

      Circle Theorems

    1. Topic 1

      Area & Perimeter

    2. Topic 2

      Circles, Arcs & Sectors

    3. Topic 3

      Volume & Surface Area

    4. Topic 4

      Congruence & Similarity

    1. Topic 1

      Right-Angled Triangles (Pythagoras & Trigonometry)

    2. Topic 2

      Sine, Cosine Rule & Area of Triangles

    3. Topic 3

      3D Pythagoras & Trigonometry

    4. Topic 4

      Trigonometric Graphs & Equations

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Basic Probability

    2. Topic 2

      Probability Diagrams (Tree & Venn Diagrams)

    3. Topic 3

      Conditional Probability

    1. Topic 1

      Averages & Range

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency

    5. Topic 5

      Scatter Graphs & Correlation