Language of Sequences & Series (DP IB Analysis & Approaches (AA): SL): Revision Note

Language of sequences & series

What is a sequence?

• A sequence is an ordered set of numbers with a rule for finding all of the numbers in the sequence

  • For example 1, 3, 5, 7, 9, … is a sequence with the rule ‘start at one and add two to each number’

• The numbers in a sequence are often called terms

  • The terms of a sequence are often referred to by the letter $u$ with a subscript

    • So in the sequence above, $u_1=1,u_2=3,u_3=5,...$

    • The n^th term is $u_n$

• If a formula for the n^th term is given, then each term in the sequence can be found by substituting the term number, $n$, into the formula

  • e.g. if $u_n=2n-1$then the 5^th term is $u_5=2\times 5-1=9$

What is a series?

• You get a series by summing up the terms in a sequence

  • E.g. For the sequence 1, 3, 5, 7, … the associated series is 1 + 3 + 5 + 7 +  …

• The notation $S_n$ is used to refer to the sum of the first $n$ terms in a series

  • $S_n=u_1+u_2+u_3+...u_n$

  • For the series above, $S_4=1+3+5+7=16$