Previously we were introduced to arithmetic and geometric sequences.

Arithmetic sequences

A sequence in which the differences\(\) of consecutive terms is constant.

​​​​​E.g., \(11,~8,~5,~2,\ldots\) has \(d=-3\)

General Term:

 \(t_n=a+(n-1)d\)

\(a\) is the first term, \(d\) is the common difference, and \(n\) is the term number.

Geometric sequences

A sequence in which the ratios of consecutive terms is constant.

E.g., \(3,-6,~12,-24,\ldots\) has \(r=-2\)

General Term:

 \(t_n=ar^{n-1}\)

\(a\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.