# Application of Geometric Sequence and Series

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 Dollar .

__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