write a program in java to print series 3,6, 12,24,48.......n
Answers
Answer:
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
Recommended: Please try your approach on {IDE} first, before moving on to the solution.
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.
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);
}