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Published online by Cambridge University Press: 05 July 2011
402. We have already remarked, that a series of numbers composed of any number of terms, which always increase, or decrease, by the same quantity, is called an arithmetical progression.
Thus, the natural numbers written in their order, as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, &c, form an arithmetical progression, because they constantly increase by unity; and the series 25, 22, 19, 16, 13, 10, 7, 4, 1, &c. is also such a progression, since the numbers constantly decrease by 3.
403. The number, or quantity, by which the terms of an arithmetical progression become greater or less, is called the difference; so that when the first term and the difference are given, we may continue the arithmetical progression to any length.
For example, let the first term be 2, and the difference 3, and we shall have the following increasing progression: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, &c., in which each term is found by adding the difference to the preceding one.
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