Sequences and Series
Sequences and Series
A sequence is a string of numbers (called terms) that follow a specific pattern. The terms in a sequence are numbered (meaning there is a first term, a second term, and so on) and are generally described with the notation an where n is the number of the term.
In an arithmetic sequence, the difference between each term is the same (a value called the common difference). For example, the sequence {20, 30, 40, 50} is arithmetic because the difference between the terms is 10. To find the next term in an arithmetic sequence, add the common value to the previous term.
\(a_{n} = a_{1} + (n\ –\ 1)d\)
where d is the common difference
In a geometric sequence, the ratio between consecutive terms is constant (a valued called the common ratio). For example, the sequence {2, 4, 8, 16, 32, 64} is geometric with a common ratio of 2. To find the common ratio, choose any term in the sequence and divide it by the previous term. To find the next term in the sequence, multiply the previous term by the common ratio.
\(a_{n} = a_{1}r^{n−1}\)
where r is the common ratio