Related Articles

# n-th term of series 1, 17, 98, 354……

• Last Updated : 27 May, 2021

Given a series 1, 17, 98, 354 …… Find the nth term of this series.
The series basically represents the sum of the 4th power of first n natural numbers. First-term is the sum of 14. Second term is sum of two numbers i.e (14 + 24 = 17), third term i.e.(14 + 24 + 34 = 98) and so on.

Examples:

```Input : 5
Output : 979

Input : 7
Output : 4676 ```

Naive Approach :
A simple solution is to add the 4th powers of first n natural numbers. By using iteration we can easily find the nth term of the series.
Below is the implementation of the above approach :

## C++

 `// CPP program to find n-th term of``// series``#include ``using` `namespace` `std;` `// Function to find the nth term of series``int` `sumOfSeries(``int` `n)``{``    ``// Loop to add 4th powers``    ``int` `ans = 0;``    ``for` `(``int` `i = 1; i <= n; i++)``        ``ans += i * i * i * i;` `    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``int` `n = 4;``    ``cout << sumOfSeries(n);``    ``return` `0;``}`

## Java

 `// Java program to find n-th term of``// series``import` `java.io.*;` `class` `GFG {` `    ``// Function to find the nth term of series``    ``static` `int` `sumOfSeries(``int` `n)``    ``{``        ``// Loop to add 4th powers``        ``int` `ans = ``0``;``        ``for` `(``int` `i = ``1``; i <= n; i++)``            ``ans += i * i * i * i;` `        ``return` `ans;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `n = ``4``;``        ``System.out.println(sumOfSeries(n));``    ``}``}`

## Python3

 `# Python 3 program to find``# n-th term of``# series`` ` `     ` `# Function to find the``# nth term of series``def` `sumOfSeries(n) :``    ``# Loop to add 4th powers``    ``ans ``=` `0``    ``for` `i ``in` `range``(``1``, n ``+` `1``) :``        ``ans ``=` `ans ``+` `i ``*` `i ``*` `i ``*` `i``      ` `    ``return` `ans`` ` ` ` `# Driver code``n ``=` `4``print``(sumOfSeries(n))`

## C#

 `// C# program to find n-th term of``// series``using` `System;``class` `GFG {` `    ``// Function to find the``    ``// nth term of series``    ``static` `int` `sumOfSeries(``int` `n)``    ``{``        ` `        ``// Loop to add 4th powers``        ``int` `ans = 0;``        ``for` `(``int` `i = 1; i <= n; i++)``            ``ans += i * i * i * i;` `        ``return` `ans;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 4;``        ``Console.WriteLine(sumOfSeries(n));``    ``}``}` `// This code is contributed by anuj_67`

## PHP

 ``

## Javascript

 ``
Output :
`354`

Time Complexity : O(n).

Efficient approach :
The pattern in this series is nth term is equal to the sum of (n-1)th term and n4.

Examples:

```n = 2
2nd term equals to sum of 1st term and 24 i.e 16
A2 = A1 + 16
= 1 + 16
= 17

Similarly,
A3 = A2 + 34
= 17 + 81
= 98 and so on..```

We get:

```A(n) = A(n - 1) + n4
= A(n - 2) + n4  + (n-1)4
= A(n - 3) + n4  + (n-1)4 + (n-2)4
.
.
.
= A(1) + 16 + 81... + (n-1)4 + n4

A(n) = 1 + 16 + 81 +... + (n-1)4 + n4
= n(n + 1)(6n3 + 9n2 + n - 1) / 30

i.e A(n) is sum of 4th powers of First n natural numbers.```

Below is the implementation of the above approach:

## C++

 `// CPP program to find the n-th``// term in series``#include ``using` `namespace` `std;` `// Function to find nth term``int` `sumOfSeries(``int` `n)``{``    ``return` `n * (n + 1) * (6 * n * n * n``                 ``+ 9 * n * n + n - 1) / 30;``}` `// Driver code``int` `main()``{``    ``int` `n = 4;``    ``cout << sumOfSeries(n);``    ``return` `0;``}`

## Java

 `// Java program to find the n-th``// term in series``import` `java.io.*;` `class` `Series {` `    ``// Function to find nth term``    ``static` `int` `sumOfSeries(``int` `n)``    ``{``        ``return` `n * (n + ``1``) * (``6` `* n * n * n``                    ``+ ``9` `* n * n + n - ``1``) / ``30``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``4``;``        ``System.out.println(sumOfSeries(n));``    ``}``}`

## Python

 `# Python program to find the Nth``# term in series`` ` `# Function to print nth term``# of series``def` `sumOfSeries(n):``    ``return` `n ``*` `(n ``+` `1``) ``*` `(``6` `*` `n ``*` `n ``*` `n``                 ``+` `9` `*` `n ``*` `n ``+` `n ``-` `1``)``/` `30``     ` `# Driver code``n ``=` `4``print` `sumOfSeries(n)`

## C#

 `// C# program to find the n-th``// term in series``using` `System;``class` `Series {` `    ``// Function to find nth term``    ``static` `int` `sumOfSeries(``int` `n)``    ``{``        ``return` `n * (n + 1) * (6 * n * n * n``                  ``+ 9 * n * n + n - 1) / 30;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 4;``        ``Console.WriteLine(sumOfSeries(n));``    ``}``}` `// This code is contributed by anuj_67`

## PHP

 ``

## Javascript

 ``
Output:
`354`

Time Complexity : O(1).

Attention reader! Don’t stop learning now. Join the First-Step-to-DSA Course for Class 9 to 12 students , specifically designed to introduce data structures and algorithms to the class 9 to 12 students

My Personal Notes arrow_drop_up