China
Africa
Explore chapters and articles related to this topic
Algebra 1
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
The terms of a series are said to be in geometric progression if the ratio of each term to its preceding term is a constant value. This ratio is known as the common ratio. For example: In the series 3, 9, 27, 81, …… the common ratio is 93=3In the series 2, −4, 8, −16, 32, ……… the common ratio is −42=−2
Sequences and series
Published in W. Bolton, Mathematics for Engineering, 2012
A geometric sequence (sometimes called a geometric progression) is one where each term is formed from the previous one by multiplying it by a constant factor. Thus if a is the first term and r the common ratio between successive terms, i.e. the multiplying factor, then the terms are: a,ar,ar2,ar3,ar4,…,etc.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
A geometric progression is a sequence in which the ratio of any term to the preceding term is a constant r. Thus, for n terms, a,ar,ar2,…,arn-1
Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem
Published in Vehicle System Dynamics, 2019
José Germán Giménez, Asier Alonso, Luis Baeza
The present subsection assesses the mesh topologies that were shown in Figure 4. The results shown in this section have been carried out by adopting derivatives obtained by finite differences and the collocation method, and presents the ratio for assessing the precision of the numerical method. The possibility of using a mesh with element size varying in geometric progression (shown in Figure 4(B)) has been analysed in Figure 14. The element size is determined by means of the following criteria: being the common ratio of the geometric progression. The results are plotted for three mesh densities as the function of the ratio between the mesh sizes of the leading and trailing elements. It can be seen in Figure 14(A) that the best results for a uniform mesh are obtained when , . However, for (Figure 14(B)) the optimal results corresponds to a ratio of the leading element size to the trailing element size, of 0.5. It should be noted in both cases that the optimal value of this parameter is independent of the mesh density used; nevertheless, its influence on the accuracy of the calculation is relatively low.