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Find the sum of series 3, -6, 12, -24 . . . upto N terms
  • Last Updated : 25 Mar, 2021

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++




//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);
}

Java




//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));
}
 
}

Python




# 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))

C#




// 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

PHP




<?php
// PHP program to find sum upto
// Nth term of the series:
// 3, -6, 12, -24, .....
 
// calculate sum upto N term of series
function Sum_upto_nth_Term($n)
{
    return (1 - pow(-2, $n));
}
 
// Driver code
$N = 5;
echo (Sum_upto_nth_Term($N));
 
// This code is contributed
// by Sach_Code
?>

Javascript




<script>
// Java program to find sum upto N term of the series:
// 3, -6, 12, -24, .....
 
// calculate sum upto N term of series
function Sum_upto_nth_Term( n) {
    return (1 - parseInt( Math.pow(-2, n)));
}
 
// Driver code
 
    let N = 5;
    document.write(Sum_upto_nth_Term(N));
 
// This code is contributed by 29AjayKumar
</script>
Output: 
33

 

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