If arithmetic progression did not exist you would not be able to count beyond 1, 2. Since 3 is the next number in the arithmetic progression. In effect there would be no arithmetic and no mathematics.
And before you cheer at the thought of one less subject to study, there would be no technology. You would still be living in a cave and have to do everything for yourself - since any kind of trade requires valuing what you have to "sell" or "buy" and that requires some form of counting.
You can use a couple different methods for this. Using Pascal's triangle you can keep making shapes that are bigger proportionally.
A rectangular number sequence is the sequence of numbers of counters needed to construct a sequence of rectangles, where the dimensions of the sides of the rectangles are whole numbers and change in a regular way. The individual sequences representing the sides are usually arithmetic progressions, but could in principle be given by difference equations, geometric progressions, or functions of the dimensions of the sides of previous rectangles in the sequence.
An arithmetic series is the sum of the terms in an arithmetic progression.
Properties of Arithmetic Mean?
who discovered in arithmetic series
everywhere!!
Aryabhatt
There is no simple answer because there is no simple rule for primes: it is certainly NOT an arithmetic progression.
Erdos' Conjecture on Arithmetic Progressions (Wikipedia.org)
You can use a couple different methods for this. Using Pascal's triangle you can keep making shapes that are bigger proportionally.
Harmonic progressions is formed by taking the reciprocals of an arithmetic progression. So if you start with some number a, and add a common difference d each time, the arithmetic progression would be a, a+d, a+2d, a+3d etc. The harmonic progression comes from taking the reciprocals of these terms. So we have a, a/(1+d), a/(1+2d), a/( 1+3d)... Here is a harmonic progression: 1/6, 1/4, 1/3, ....
There is no simple answer. There are simple formulae for simple sequences such as arithmetic or geometric progressions; there are less simple solutions arising from Taylor or Maclaurin series. But for the majority of sequences there are no solutions.
Progressions of Power was created in 1979-12.
A rectangular number sequence is the sequence of numbers of counters needed to construct a sequence of rectangles, where the dimensions of the sides of the rectangles are whole numbers and change in a regular way. The individual sequences representing the sides are usually arithmetic progressions, but could in principle be given by difference equations, geometric progressions, or functions of the dimensions of the sides of previous rectangles in the sequence.
Gauss
Nancy Anne Hastings has written: 'Secondary progressions' -- subject(s): Astrology, Progressions (Astrology)
The nouns are kind, music, chord, and progressions: each word is the name of something.