Working with Sequences and Series - Definition and finding the nth term

Working with Sequences and Series - Definition and finding the nth term

Understanding Sequences and Series

  • A sequence is a list of numbers arranged in a fixed order.
  • Each number in a sequence is called a term.
  • The position of a term in a sequence is called its index or rank.
  • The last element of a finite sequence is referred to as the end term of the sequence.
  • A series is the sum of the terms of a sequence.

Identifying the nth Term

  • To find the nth term, you need to find a rule that gives you the term in the nth position in a sequence.
  • For example, in the sequence 2, 4, 6, 8, the nth term would be (2n), because when you multiply the position of each term by 2, you get the term itself.
  • Sometimes, the nth term requires a bit more complexity – it might involve squares or higher powers.

Working with Arithmetic Sequences

  • An arithmetic sequence is a sequence of numbers where the difference between successive terms is constant.
  • This difference is called the common difference.
  • The nth term of an arithmetic sequence can be found using the formula: (a + (n-1)d), where ‘a’ is the first term and ‘d’ is the common difference.

Working with Geometric Sequences

  • A geometric sequence is a sequence of numbers where the ratio of successive terms is constant.
  • This ratio is referred to as the common ratio.
  • The nth term of a geometric sequence can be found using the formula: (ar^{(n-1)}), where ‘a’ is the first term and ‘r’ is the common ratio.

Revising Sequences and Series

  • Be able to understand the distinction between a sequence and a series.
  • Develop an understanding of the different rules to calculate the nth term in both arithmetic and geometric sequences.
  • become familiar with the common difference in arithmetic sequences and the common ratio in geometric sequences.

Deepening Understanding of Sequences and Series

  • Practice a variety of problems involving sequences and series.
  • Difficult questions might involve sequences with square or higher-powered terms.
  • Use a range of resources and past papers for deeper understanding and familiarity with different types of problems involving sequences and series.

Remember, regular practice can enhance your understanding and ability to work with sequences and series.