Table of Contents

**What is Arithmetic Mean?**

The arithmetic mean, also known as the average or the Mean, is a fundamental concept in mathematics. It is the sum of all the numbers in a set divided by the no. of items in the set. It is the sum of all the numbers in the set divided by the total number of items.

The arithmetic mean is typically used to measure the tendency of a set of numbers. It is one of the most generally used measures of central tendency, along with the median and the mode. It is also used to compare sets of numbers or the results of different experiments. The arithmetic mean is not the only type of Mean. Other means include the geometric Mean, harmonic Mean, and root mean square. Each of these has different uses and applications.

The arithmetic mean is also used to measure the average rate of change in a set of numbers. The arithmetic mean can also be used to measure the standard deviation of a group of numbers. The standard deviation measures how much a set of numbers deviates from the Mean.

**What is Geometric Sequence?**

A geometric sequence is a series of nos in which each successive number is obtained by multiplying the preceding number by a fixed, non-zero number. This number is known as the standard ratio of the sequence.

Geometric sequences can be written as a, ar, ar^2, and ar^3, where a is the first term in the series and r is the standard ratio. The typical ratio must be a number other than zero, and it determines whether the sequence increases or decreases. If r is greater than one, the series will increase; if it is less than one, the sequence will decrease.

The totality of the first n terms is given by the formula a(r^n-1) / (r – 1). This formula can find the sum of any number of terms in the sequence. Geometric sequences have many applications in mathematics, science, and engineering. They are often used to model population growth, radioactive decay, and other exponential functions. They can also calculate compound interest and model object movement in physics.

**Differences Between Arithmetic Mean and Geometric Sequence**

- Arithmetic Mean is the average of a set of numbers. In contrast, a geometric Sequence is a sequence of numbers where each successive number is equal to the previous number multiplied by a common factor.
- Arithmetic Mean is figured by adding all the numbers in the set and dividing by the total number of items; a Geometric Sequence is calculated by multiplying each number in the sequence by a fixed factor.
- Arithmetic Mean is calculated by adding all numbers and dividing by the total number. In contrast, Geometric Sequence is calculated by multiplying each number in the sequence by the common factor.
- Arithmetic Mean is used to measure the average of a group of numbers, while Geometric Sequence is used to measure the growth rate of the numbers in a sequence.
- Arithmetic Mean is affected by outliers, while Geometric Sequence is not affected by outliers.

**Comparison Between Arithmetic Mean and Geometric Sequence**

Parameters of comparison | Arithmetic Mean | Geometric Sequence |

Rate of growth | Linear | Exponential |

Value | It is a single value. | It is a set of values. |

Used to measure | It is used to measure central tendency. | It is used to measure the rate of change. |

Estimates | It measures the average of a group of numbers. | It measures the growth rate of the numbers in a sequence. |

Used in | Descriptive statistics. | Predictive analytics. |