Which type of series is defined by a fixed common difference?

Which type of series is defined by a fixed common difference?

• A. Geometric series
• B. Harmonious series
• C. Arithmetic series
• D. Trigonometric series

Answer: (C)

An arithmetic series is defined by a fixed common difference between consecutive terms. In this type of series, each term is derived from the previous term by adding a constant value, known as the common difference. For example, if the first term is \( a \) and the common difference is \( d \), the terms of the series can be expressed as \( a, a+d, a+2d, a+3d, \) and so forth. The defining characteristic of an arithmetic series is that the difference between any two successive terms remains constant throughout the series. In contrast, a geometric series involves a common ratio rather than a common difference, meaning each term is obtained by multiplying the previous term by a fixed constant. A harmonious series, often referred to in terms of harmonics, is related to the sum of the reciprocals of natural numbers rather than a simple arithmetic pattern. Lastly, trigonometric series revolve around functions of angles and do not adhere to a fixed difference or ratio paradigm. Therefore, the clear definition of an arithmetic series aligns perfectly with the criterion of having a fixed common difference.

An arithmetic series is defined by a fixed common difference between consecutive terms. In this type of series, each term is derived from the previous term by adding a constant value, known as the common difference. For example, if the first term is ( a ) and the common difference is ( d ), the terms of the series can be expressed as ( a, a+d, a+2d, a+3d, ) and so forth. The defining characteristic of an arithmetic series is that the difference between any two successive terms remains constant throughout the series.

In contrast, a geometric series involves a common ratio rather than a common difference, meaning each term is obtained by multiplying the previous term by a fixed constant. A harmonious series, often referred to in terms of harmonics, is related to the sum of the reciprocals of natural numbers rather than a simple arithmetic pattern. Lastly, trigonometric series revolve around functions of angles and do not adhere to a fixed difference or ratio paradigm. Therefore, the clear definition of an arithmetic series aligns perfectly with the criterion of having a fixed common difference.