The Louvre Museum as seen through the Louvre Pyramid glass in Paris, France. From the National Geographic book The 10 Best of Everything. Smithsonian Institution, Washington, D.C. The Smithsonian is the worldâs largest research and museum complex, with 19 museums and galleries, the National Zoological Park, and various research stations.
1 An arithmetic sequence is a sequence with the difference between two consecutive terms constant. 2  The difference is called the common difference. 3  A geometric sequence is a sequence with the ratio between two consecutive terms constant. 4  This ratio is called the common ratio.
Geometric sequences and series. A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r. Example. Write the first five terms of a geometric sequence in which a 1 =2 and r=3. We use the first given formula: Just as with arithmetic series it is possible to find the sum of a geometric series. It is found by using one of the following formulas: Videolesson: use the formula for the sum of a geometric series to determine the sum when a 1 =4 and r=2 and we have 12 terms. 1  Pre-Algebra. 2  Algebra 1. 3  Algebra 2. 4  Geometry.