In this tutorial we discuss about the related problems of application of geometric sequence and geometric series.

Example:
            A line is divided into six parts forming a geometric sequence. If the shortest length is cm and the longest is cm, find the length of the whole line.
Solution:
                        Given that
                        , ,
            Since     we have
                           
            For the length of the whole line, we have
                               (As )
                        cm
            Therefore, the whole length of the line is equal to cm.

Example:
            The value of an automobile depreciates at the rate of per year. What will be the value of an automobile after three years hence which is now purchased for.
Solution:
            Let  = purchased value of the automobile.
            The value of automobile at the end of first year
                       
            The value of automobile at the end of second year
                       
                       
            Similarly, the value at the end of third year
                       
            Hence, the value of the automobile at the end of years hence now purchased for
                       

Example:
            At  compounded annually, find the compound amount of at the end of years.
Solution:
            Amount after first year      
                                                    
            Amount after second year
            Amount after third year     
            It becomes a G.P., in which , ,