Find the sum of series 3, 6, 12, 24 . . . upto N terms (original) (raw)

Last Updated : 11 Jul, 2025

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 #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

JavaScript

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Time Complexity: O(logn), where n is the given integer.

Auxiliary Space: O(1), no extra space is required, so it is a constant.