define the following terms: series,progression, arithmetic progression, geometric progressions and harmonic progressions
Answers
series:
a number of events, objects, or people of a similar or related kind coming one after another.
"the explosion was the latest in a series of accidents"
progression:
the process of developing or moving gradually towards a more advanced state.
"good opportunities for career progression"
arithmetic progression:
a sequence of numbers in which each differs from the preceding one by a constant quantity (e.g. 1, 2, 3, 4, etc.; 9, 7, 5, 3, etc.).
geometric progressions:
a progression of numbers with a constant ratio between each number and the one before (e.g. 1, 3, 9, 27, 81).
harmonic progression:
1.MUSIC
a series of chord changes forming the underlying harmony of a piece of music.
2.MATHEMATICS
a sequence of quantities whose reciprocals are in arithmetical progression (e.g. 1, 1/3, 1/5, 1/7, etc.).
Series: A series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers, but much more generality is possible.
Progression: A progression is a series that advances in a logical and predictable pattern.
Arithmetic progression: An arithmetic progression is a sequence of numbers in which each successive term is the sum of its preceding term and a fixed number.
Geometric progression: A geometric progression is a sequence where every term bears a constant ratio to its preceding term.
Harmonic progression: A harmonic progression is a sequence obtained by taking the reciprocal of the terms of an arithmetic progression.