Sentence examples for an arithmetic progression from inspiring English sources

In number theory, an arithmetic progression is a sequence of numbers that proceeds in steps of the same amount.

The increase of population will take place, if unchecked, in a geometric progression, while the means of subsistence will increase in only an arithmetic progression.

In a real farce, the protagonist lies to save his skin; his duplicity multiplies by an arithmetic progression until he's driven almost out of his mind by self-consciousness.

Precisely, there exists a unitary equivalenceΔ=R+Q−1where [R, Q−1]=0, where the spectrum ofRlies on an arithmetic progression and whereQ−1is a pseudodifferential operator of order −1.

We also have a bonus puzzle this week — an arithmetic progression challenge suggested by Dr. Graham, which he phrases as follows: Call a set of 3 integers a < b < c "evenly spaced" if b-a = c-b.

Van der Waerden's theorem states that if the positive integers are divided into any finite number of disjoint sets (i.e., sets without any members in common) and k is an arbitrary positive integer, then at least one of the sets contains an arithmetic progression of length k.

The same Dirichlet (who reportedly kept a copy of Gauss's Disquisitiones Arithmeticae by his bedside for evening reading) made a profound contribution by proving that, if a and b have no common factor, then the arithmetic progression a, a + b, a + 2b, a + 3b, … must contain infinitely many primes.

For instance, the facet indexes at each row of the top right quadrant follow the arithmetic progression a(i =a(i−1) + 6.

Similarly, notice that 4.1, 4.3, 4.4, 4.5 are all arithmetic progressions mod 5, with common differences 1, 2, 3, 4, respectively.

The scheme is comprised of an uneven clustering algorithm based on arithmetic progression, a cover set partition algorithm based on trust and a node scheduling algorithm based on energy prediction.

In other words, they form a three-term arithmetic progression.