DescriptionSequences and series involve lists of numbers and their sums. The numbers in the list may be generated by a pattern of addition, subtraction, multiplication, or division. An ordered list of numbers is called a sequence. A sequence could represent the distance a person runs each week as they train to run a race or an employee's salary over a set of years. The sum of the numbers in a sequence is a series. A series could represent all the miles a person runs while training for a race or all the money an employee earns over a set of years.
At A Glance
- A sequence is a list of numbers that follows a pattern. Sequences can be defined using recursive or explicit rules.
- In an arithmetic sequence, consecutive terms differ by the same number, called the common difference.
- In a geometric sequence, the ratio of consecutive terms is the same number, called the common ratio.
- Some sequences are neither arithmetic nor geometric, such as the Fibonacci sequence, which models many natural phenomena.
- A series is the sum of terms of a sequence. A sum of terms can be written using summation notation.
- A formula can be used to find the sum of a finite arithmetic series.
- A formula can be used to find the sum of a finite geometric series.
- The sum of an infinite series may be found by using partial sums.