A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non - zero number called the common ratio. For example, the sequences 2, 6, 18, . ... 3, 15, 75 , …. are a geometric sequences with common ratios 3 and 5 respectively. A geometric sequence is generally characterized by three numbers, the first term ‘ a’, the common ratio ‘ r’ and the number of terms ‘ n’. A geometric series is the sum of numbers in a geometric sequence. 2+ 6+ 18 and 3+ 15+ 75 are examples of geometric series with three terms each. The nth term of a geometric series with initial value ‘ a’ and common ratio ‘ r’ is given by: ?? = ???−1. While the sum of a geometric series is given by: ?(1-??−1) / 1-??−1 Create a class Geometric Series to model a Geometric series. Using friend function, overload the ‘~’ operator to find the nth term of the series. Likewise, overload the ‘!’ operator (using a friend function) to find the sum of a Geometric series. Provide a function display() in the class to display the geometric series. Sample output of the program should be like the following. Sample Program Output GeometricSeries series (1,2,4); cout<<"Nth term is: "<<~series<
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non - zero number called the common ratio. For example, the sequences
2, 6, 18, . ...
3, 15, 75 , ….
are a geometric sequences with common ratios 3 and 5 respectively. A geometric sequence is generally characterized by three numbers, the first term ‘ a’, the common ratio ‘ r’ and the number of terms ‘ n’. A geometric series is the sum of numbers in a geometric sequence. 2+ 6+ 18 and 3+ 15+ 75 are examples of geometric series with three terms each.
The nth term of a geometric series with initial value ‘ a’ and common ratio ‘ r’ is given by: ?? = ???−1. While the sum of a geometric series is given by:
?(1-??−1) / 1-??−1
Create a class Geometric Series to model a Geometric series. Using friend function, overload the ‘~’ operator to find the nth term of the series. Likewise, overload the ‘!’ operator (using a friend function) to find the sum of a Geometric series.
Provide a function display() in the class to display the geometric series. Sample output of the program should be like the following.
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Sample Program |
Output |
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GeometricSeries series (1,2,4); cout<<"Nth term is: "<<~series<<endl; cout<<"Sum of series is: "<<!series<<endl; cout<<”The complete series is: "<<endl; series.display(); |
Nth term is: 8 Sum of series is: 15 The complete series is: 1+2+4+8 |
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