Find the sum of series 3, -6, 12, -24 . . . upto N terms

Given an integer N. The task is to find the sum upto N terms of the given series:

3, -6, 12, -24, … upto N terms

Examples:

Input : N = 5
Output : Sum = 33

Input : N = 20
Output : Sum = -1048575


On observing the given series, it can be seen that the ratio of every term with their previous term is same which is -2. Hence the given series is a GP(Geometric Progression) series.

You can learn more about GP series here.

So, S_{n} = \frac{a(1-r^{n})}{1-r} when r < 0.

In above GP series the first term i:e a = 3 and common ratio i:e r = (-2).

Therefore, S_{n} = \frac{3(1-(-2)^{n})}{1-(-2)}.
Thus, S_{n} = 1-(-2)^{n}.

Below is the implementation of above approach:

C++

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//C++ program to find sum upto N term of the series:
// 3, -6, 12, -24, .....
  
#include<iostream>
#include<math.h>
using namespace std;
//calculate sum upto N term of series
  
class gfg
{
    public:
    int Sum_upto_nth_Term(int n)
    {
        return (1 - pow(-2, n));
    }
};
// Driver code
int main()
{
    gfg g;
    int N = 5;
    cout<<g.Sum_upto_nth_Term(N);
}

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Java

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//Java program to find sum upto N term of the series:
// 3, -6, 12, -24, .....
  
import java.util.*;
//calculate sum upto N term of series
  
class solution
{
  
static int Sum_upto_nth_Term(int n)
{
    return (1 -(int)Math.pow(-2, n));
}
  
// Driver code
public static void main (String arr[])
{
    int N = 5;
    System.out.println(Sum_upto_nth_Term(N));
}
  
}

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Python

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# Python program to find sum upto N term of the series:
# 3, -6, 12, -24, .....
  
# calculate sum upto N term of series
def Sum_upto_nth_Term(n):
    return (1 - pow(-2, n))
  
# Driver code
N = 5
print(Sum_upto_nth_Term(N))

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C#

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// C# program to find sum upto 
// N term of the series:
// 3, -6, 12, -24, .....
  
// calculate sum upto N term of series
class GFG
{
  
static int Sum_upto_nth_Term(int n)
{
    return (1 -(int)System.Math.Pow(-2, n));
}
  
// Driver code
public static void Main()
{
    int N = 5;
    System.Console.WriteLine(Sum_upto_nth_Term(N));
}
}
  
// This Code is contributed by mits

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PHP

Output:

33


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