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.
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. Examples of a geometric sequence are powers r of a fixed number r, such as 2 and 3.The general form of a geometric sequence is., â3, 9, â27, 81, â243, ... is a geometric sequence with common ratio â3. The behaviour of a geometric sequence depends on the value of the common ratio. If the common ratio is: 1  Positive, the terms will all be the same sign as the initial term.