Get Arithmetic And Geometric Sequences Practice Homework

A progression in Mathematics is a series of numbers that exhibits a particular pattern. An arithmetic progression is a series where the difference between any two adjacent terms is one and the same. Similarly, a geometric progression is one where any two consecutive terms are related by the common ratio.

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms.

If we multiply or divide by the same number each time to make the sequence, it is a geometric sequence. The common ratio is the same for any two consecutive terms in the same sequence. 3 , 9 , 27 , 81 , 243 , . . .

The difference between a progression and a sequence is thata progression has a specific formulato calculate its nth term, whereas a sequence can be based on a logical rule like 'a group of prime numbers'. For example: {2, 4, 6, 8, 10} is a progression. Its nth term is 2n.

The arithmetic mean is the most commonly used type of mean and is often referred to simply as “the mean.” While the arithmetic mean is based on adding and dividing values, the geometric mean multiplies and finds the root of values.

Types of Progressions ProgressionDefinition Arithmetic Progression (AP) The differences between any two consecutive numbers are all same. Geometric Progression (GP) The ratios of any two consecutive numbers are all same. Harmonic Progression (HP) The reciprocals of terms form an AP.

Arithmetic sequences are defined by an initial value and a common difference, with the same number added or subtracted to each term. Geometric sequences are defined by an initial value and a common ratio, with the same number multiplied or divided to each term.

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms.