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,
In above GP series the first term i:e a = 3 and common ratio i:e r = (-2).
Therefore,
Thus,
Below is the implementation of above approach:
//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 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 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# 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 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 ?> |
<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
Time Complexity: O(logn), where n is the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.