examples of arithmetic and geometric sequences

An arithmetic sequence is a list of numbers with a definite pattern.If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence. Give the common difference or ratio, if it exists. Jennifer Freidenreich Diablo Valley College Geometric sequences have a common ratio. The two simplest sequences to work with are arithmetic and geometric sequences. For instance, the sequenceĠ 1, 1 2, 2 4, 3 8, 4 16, 5 32, ⋯. Definition and Basic Examples of Arithmetic Sequence. Categorize the sequence as arithmetic, geometric, or neither. Arithmetico-geometric sequences arise in various applications, such as the computation of expected values in probability theory. An arithmetic sequence is a number sequence calculated by subtracting or adding a fixed term to/from the previous term. Main Differences Between Arithmetic and Geometric Sequence.

Put plainly, the nth term of an arithmetico-geometric sequence is the product of the nth term of an arithmetic sequenceĪnd the nth term of a geometric one. For example, the sequence 3, 6, 12, 24, and so on is a geometric sequence with the standard ratio being 2. In mathematics, arithmetico-geometric sequence is the result of term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression. Practice identifying both of these sequences by watching this tutorial Keywords: sequence arithmetic sequence geometric sequence common ratio common.

Examples of arithmetic and geometric sequences