Arithmetic progression

An arithmetic progression is a sequence in which the difference between each pair of consecutive terms is constant. Its terms increase, decrease, or remain fixed according to that common difference.

Common difference: The fixed amount added to each term of an arithmetic progression to obtain the next term. This value defines the progression and determines whether its terms rise, fall, or stay fixed.
Sequence: An ordered list of numbers or other mathematical objects indexed by position. An arithmetic progression is a sequence distinguished by its constant consecutive difference.
Gauss's trick: A method for summing an arithmetic sequence by pairing terms from opposite ends. The pairing makes each pair sum to the same value, simplifying the total.
Geometric sequence: A sequence in which each term after the first is obtained by multiplying by a fixed ratio. Geometric sequences keep a ratio constant, unlike the fixed difference here.
Arithmetic sequence formula: The formula for the nth term of an arithmetic progression: the first term plus n minus one times the common difference. It calculates any term directly without listing the terms before it.
Term (mathematics): An individual element of a sequence or sum, identified by its position or index. The common difference relates each term to the term immediately before it.
Triangular number: A number equal to the sum of the positive integers from one through a given integer. Its defining sum is a finite arithmetic progression with common difference one.
Harmonic progression: A sequence of nonzero terms whose reciprocals form an arithmetic progression. Its equal spacing appears in reciprocal values, not in the terms themselves.
Arithmetic series: The sum of the terms in a finite or infinite arithmetic progression. Pairing terms from opposite ends gives a concise formula for a finite sum.
Index (mathematics): A number that identifies a position in an ordered sequence or indexed collection. The term formula uses the index to locate a term without generating earlier terms.

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