arithmetic progression farâyâzi-yz hesâbi (#) Fr.: progression arithmétique A → sequence of n numbers or quantities such that the difference between any two successive terms is a constant. In particular, if a is the first term, the nth term is a + (n - 1)d, where d is the constant. Also called → arithmetic sequence. → arithmetic; → progression. |
geometric progression farâyâsi-e hendesi (#) Fr.: progression géométrique A → sequence in which the ratio of a term to its predecessor is the same for all terms. In general, the nth term has the form ar^{(n-1)}, where n is a positive integer, and a and r are nonzero constants; r is called the ratio or common ratio. The sum of the first n terms is given by: S_{n} = a(1 - r^{n})/(1 - r). Also called → geometric sequence. → geometric; → progression. |
harmonic progression farâyâzi-ye hamâhang Fr.: progression harmonique Math.: Any ordered set of numbers, the reciprocals of which have a constant difference between them. For example 1, ½, 1/3, ¼, ..., 1/n. Also called → harmonic sequence. → harmonic; progression. |
progression farâyâzi (#) Fr.: progression Math.: A succession of numbers or quantities in which there is a constant relation between each member and the one succeeding it. See also → arithmetic progression, → geometric progression, → harmonic progression. From O.Fr. progression, from L. progressionem "a going forward," from progressus, p.p. of progredi "go forward," from → pro- "forward" + gradi "to step, walk," from gradus "step." Farâyâzi, from farâ-, → pro-, + yâzi, verbal noun of yâzidan "to stretch out the arms; grow up;" Parthian Mid.Pers. y'd "to reach a goal, come to, stretch out;" Av. yat- to reach, take one's place," yaiiata "places,' frā-iiatāt "has reached;" cf. Skt. yat- "to be in place, put in place, line up;" PIE base *iet- "to be in place." |