Find the sum of the series 2, 5, 13, 35, 97... (original) (raw)

Last Updated : 23 Dec, 2022

Given a series and a number n, the task is to find the sum of its first n terms. Below is the series:

2, 5, 13, 35, 97, ...

Examples:

Input: N = 2 Output: 7 The sum of first 2 terms of Series is 2 + 5 = 7

Input: N = 4 Output: 55 The sum of first 4 terms of Series is 2 + 5 + 13 + 35 = 55

Approach: From this given series we find it is the sum of the Two GP series with common ratios 2, 3.

Sn = 2 + 5 + 13 + 35 + 97 ... + upto nth term
Sn = (2^0 + 3^ 0) + (2^1 + 3^1) + (2^2 + 3^2) + (2^3 + 3^3)+ (2^4 + 3^4) …… + upto nth term
Sn = (2^0 + 2^1 + 2^2 + 2^3 + 2^4 ... + upto nth term) + ( 3^0 + 3^1 + 3^2 + 3^3 …… + unto nth term )

Since We know that the sum of n terms of the GP is given by the following formula:
Sn=fraca(rn−1)(r−1)S_n=\frac{a(r^n-1)}{(r-1)}Sn=fraca(rn−1)(r−1)

Below is the implementation of the above approach:

C++ `

// C++ program for finding the sum // of first N terms of the series. #include <bits/stdc++.h> using namespace std;

// CalculateSum function returns the final sum int calculateSum(int n) { // r1 and r2 are common ratios // of 1st and 2nd series int r1 = 2, r2 = 3;

// a1 and a2 are common first terms
// of 1st and 2nd series
int a1 = 1, a2 = 1;

return a1 * (pow(r1, n) - 1) / (r1 - 1)
       + a2 * (pow(r2, n) - 1) / (r2 - 1);

}

// Driver code int main() { int n = 4;

// function calling for 4 terms
cout << "Sum = " << calculateSum(n)
     << endl;

return 0;

}

Java

//Java program for finding the sum //of first N terms of the series.

public class GFG {

//CalculateSum function returns the final sum
static int calculateSum(int n)
{
 // r1 and r2 are common ratios
 // of 1st and 2nd series
 int r1 = 2, r2 = 3;

 // a1 and a2 are common first terms
 // of 1st and 2nd series
 int a1 = 1, a2 = 1;

 return (int)(a1 * (Math.pow(r1, n) - 1) / (r1 - 1)
        + a2 * (Math.pow(r2, n) - 1) / (r2 - 1));
}

//Driver code
public static void main(String[] args) {
    
    int n = 4;

     // function calling for 4 terms
     System.out.println("Sum = " +calculateSum(n));
}

}

Python 3

Python 3 program for finding the sum

of first N terms of the series.

from math import everything

from math import *

CalculateSum function returns the final sum

def calculateSum(n) :

# r1 and r2 are common ratios 
# of 1st and 2nd series 
r1, r2 = 2, 3

# a1 and a2 are common first terms 
# of 1st and 2nd series 
a1, a2 = 1, 1

return (a1 * (pow(r1, n) - 1) // (r1 - 1) 
       + a2 * (pow(r2, n) - 1) // (r2 - 1))

Driver Code

if name == "main" :

n = 4

# function calling for 4 terms
print("SUM = ",calculateSum(n))

This code is contributed by ANKITRAI1

C#

// C# program for finding the sum // of first N terms of the series. using System;

class GFG {

// CalculateSum function // returns the final sum static int calculateSum(int n) { // r1 and r2 are common ratios // of 1st and 2nd series int r1 = 2, r2 = 3;

// a1 and a2 are common first // terms of 1st and 2nd series int a1 = 1, a2 = 1;

return (int)(a1 * (Math.Pow(r1, n) - 1) / (r1 - 1) + a2 * (Math.Pow(r2, n) - 1) / (r2 - 1)); }

// Driver code static public void Main () { int n = 4;

// function calling for 4 terms
Console.Write("Sum = " +
               calculateSum(n));

} }

// This code is contributed by Raj

PHP

JavaScript

`

Time Complexity: O(log n)
Auxiliary Space: O(1), As constant extra space is used.