Sequences Summary

Sequences

Summary

a sequence is a set of numbers arranged in a particular order.

sequences can be shown in any of four ways:

  • by listing
  • by formula
  • by recursive function
  • by graph

the greek letter capital sigma, ∑ can be used to show that a sequence of numbers have to be added together.

a mathematical series is obtained by adding the terms of a sequence together.

think of ∑ as meaning "the sum of".

the terms of a convergent sequence tend towards a limit.

 

Key Skills
  • find subsequent terms of a sequence given the first three or four terms
  • find terms of a sequence given the general term
  • list a sequence given the recursive function
  • evaluate sums involving sigma notation
  • express a given series in sigma notation
  • understand the behaviour of a convergent sequence

Vocabulary

sequence, finite sequence, infinite sequence, arithmetic sequence, geometric sequence, term, recursive function, convergent, divergent, limit.