Arithmetic Sequences (Edexcel IGCSE Maths A (Modular))

Arithmetic Sequences

What is an arithmetic sequence?

• An arithmetic sequence is a sequence where terms increase by the same amount each time

  • The amount it increases by is called the common difference

    • For example: 3, 5, 7, 9, ...

    • The common difference is 2

• Common differences can be negative

  • These arithmetic sequences decrease by the same amount each time

    • For example: 11, 8, 5, 2, -1, ...

    • The common difference is -3

• Arithmetic sequences are also called linear sequences

What is the formula for the nth term of an arithmetic sequence?

• The formula for the ^th term of an arithmetic sequence is

  

  • is the first term

  • is the common difference

  • is the ^th term

    • e.g. gives the fifth term,

How do I use the formula for the nth term of an arithmetic sequence?

• You can substitute in the values of , and to find a particular term

  • e.g. , and gives

    • So 18 is the 3^rd term

• You can substitute in the values of and to find an expression for

  • e.g. and gives

    • This simplifies to

• You can form equations in terms of and if given information about terms

  • e.g. If the 5^th term is 11,

    • giving

    • This simplifies to

  • Forming two different equations in and can lead to simultaneous equations