Arithmetic and geometric sequences and their summations - (7.1-7.3)

Understand the concept and the properties of arithmetic sequences

  • Theory
    An Arithmetic Sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
    For example, 4, 7, 10, 13, .....
    We notice numbers above show predictable patterns. Each sucessive number is greater than the previous one by 3. Hence, it is an arithmetic Sequence
    To find out the \(n^{th}\) term of an Arithmetic Sequence, the general term of is given by \(T_n=a+(n-1)d\),
    • where \(T_n\) is the \(n^{th}\) term of the sequence,
    • a is the first term of the sequence
    • n denote the number of term
    • d denote the common difference
    Referring to examples above,
    a is the first term of the sequnence, which is 4
    d is the common difference, which is 3
    13 is the fourth term of the sequence, \(\therefore n=4, T_4=13\)
  • Examples
    If the \(9^{th}\) term and the \(11^{th}\) term of an Arithmetic Sequence is 52 and 22. Find the first term and common difference of the Sequence.
  • Solutions

Understand the general term of an arithmetic sequence

  • Theory
  • Examples
  • Solutions

Understand the concept and the properties of geometric sequences

  • Graph
  • Theory
  • Examples
  • Solutions