Assignment: The sum $\backslash ($ S$\_\{$n$\}\backslash )$ of the first $\backslash ($ n $\backslash )$ terms of a geometric series is:

$\backslash [$

S$\_\{$n$\}=$a$+$a r$+$a r$^\{2\}+$a r$^\{3\}+\backslash$ldots$+$a r$^\{$n$-1\}$

$\backslash ]$

where $\backslash ($ a $\backslash )$ is the first term of the series and $\backslash ($ r $\backslash )$ is called the common ratio.

Your task is to write a public class that uses recursion to compute the sum of the first $\backslash ($ n $\backslash )$ terms of a geometric series. Write a class named GeometricSeries that includes:

$-$ A recursive public static double method called geometricSum $($int $\backslash ($ n $\backslash ),$ double a$,$ double $\backslash ($ r $\backslash ))$ which calculates the sum of the first $\backslash ($ n $\backslash )$ terms of the geometric series for given $\backslash ($ a $\backslash )$ and $\backslash ($ r $\backslash )$;

$-$ A main method in your GeometricSeries class that: should terminate;

$-$ displays the message "Enter a value for the first term: $"$ and allows the user to input a double value $\backslash ($ a $\backslash )$;

$-$ displays the message "Enter a value for the connon ratio: $"$ and allows the user to input a double value $\backslash ($ r $\backslash )$;

$-$ invokes the geometricSun method and then displays the following message:

The sum of the first $[$n$]$ terms is $[$sum$]$

For example, if $\backslash ($ n$=4,$ a$=1\backslash ),$ and $\backslash ($ r$=2\backslash ),$ the final message should be:

The sum of the first $4$ terms is $15\mathrm{.}0$