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 Everyday Examples
Geometric Sequence:  A sequence of numbers in which the ratio between any two consecutive terms is the same. In other words, you multiply by the same number each time to get the next term in the sequence. This fixed number is called the common ratio for the sequence.
 Image source: http://www.state.de.us/sos/money.gif The value of an untouched bank account, such as a CD or bond, forms a geometric sequence because the value in the account increases by a common multiple each year. For example, a \$1000 account earning 3% each year, will have 1000*1.03 = \$1030 after the first year; 1030*1.03 = \$1060.90 after the second year; 1060.90*1.03 = \$1092.73 after the third year; and so on. Image source: http://www.colorado.edu/ScienceDiscovery/convection/images/balloon.jpg The height of a hot air balloon over time represents a geometric sequence because its change in elevation is a certain percentage of its previous height. For example, suppose a balloon reaches a height of 200 feet for its first minute, and continues to rise 40% of its previous height for the remainder of the flight. That means after the first minute, it will rise 200*0.40 = 80 more feet; after the second minute, it will rise 80*0.40 = 32 more feet; and so on.