GeeksforGeeks App
Open App
Browser
Continue

# Find the sum of N terms of the series 1, 4, 13, 40, 121, …

Given a positive integer, n. Find the sum of the first n term of the series:

1, 4, 13, 40, 121, …..

Examples:

Input: n = 5
Output: 179

Input: n = 3
Output: 18

Approach:

The sequence is formed by using the following pattern. For any value N-

The above solution can be derived following the series of steps-

Let Tn be the nth term and Sn be the sum to n terms of the given series.

Thus, we have

-(1)

Equation (1) can be written as-

S_{n}=1+4+13+40+121+…+T_{n-1}+T_{n}  -(2)

Subtracting equation (2) from equation (1), we get

The above equation 3, 9, 27, 81, … is a G.P. with common ratio 3 and first term 3.

Thus, we have

Since,

Therefore,

Thus, sum of n terms is

Illustration:

Input: n = 5
Output: 179
Explanation:

=
=
=179

Below is the implementation of the above approach:

## C++

 // C++ program to implement// the above approach#include using namespace std; // Function to return sum of// first N term of the seriesint findSum(int N){    return (pow(3, N + 1) -                3 - 2 * N) / 4;} // Driver Codeint main(){    int N = 5;    cout << findSum(N);    return 0;}

## Java

 // Java program for the above approachimport java.util.*;public class GFG{   // Function to return sum of  // first N term of the series  static int findSum(int N)  {    return (int)(Math.pow(3, N + 1) -                 3 - 2 * N) / 4;  }   public static void main(String args[])  {    int N = 5;    System.out.print(findSum(N));  }}// This code is contributed by Samim Hossain Mondal.

## Python3

 # Python code for the above approach # Function to return sum of# first N term of the seriesdef findSum(N):    return (3 ** (N + 1) - 3 - 2 * N) // 4; # Driver CodeN = 5;print(findSum(N)); # This code is contributed by Saurabh Jaiswal

## C#

 // C# program to implement// the above approachusing System;class GFG{ // Function to return sum of// first N term of the seriesstatic int findSum(int N){    return (int)(Math.Pow(3, N + 1) -                3 - 2 * N) / 4;}   // Driver Code  public static void Main()  {    int N = 5;    Console.Write(findSum(N));   }} // This code is contributed by Samim Hossain Mondal.

## Javascript

 

Output

179

Time Complexity: O(log3N) because using inbuilt pow function

Auxiliary Space: O(1)

My Personal Notes arrow_drop_up