# Application of Geometric Sequence and Series

In this tutorial we discuss 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 the value of an automobile be after three years if it is purchased for dollars?

__Solution__:

Let = purchased value of the automobile.

The value of automobile at the end of the first year

The value of the automobile at the end of the second year

Similarly, the value at the end of the third year

Hence, the value of the automobile at the end of years after being purchased for