Program to find N-th term of the series a, b, b, c, c, c,…….

• Difficulty Level : Medium
• Last Updated : 13 Mar, 2023

Given a number N. The task is to write a program to find the N-th term in the below series:

`a, b, b, c, c, c, d, d, d, d, .....`

Examples:

```Input : 12
Output : e

Input : 288
Output : x```

The idea is to use AP sum formula to find the solution to this problem. Clearly the series is depicted as 1a, 2b’s, 3c’s, 4d’s, 5e’s and so on. Thus making it an AP. Now we can use the AP sum formula:

`sum = (n/2)*(a + (n-1)*d)  `

Which in this case becomes sum = (n(n+1))/2( since a = 1 and d = 1 ) where ‘sum’ here is the Nth term given.

Below is the implementation of the above approach:

C++

 `// CPP program to find nth term of the``// given series``#include ``using` `namespace` `std;`` ` `// Function to find nth term of the``// given series``void` `findNthTerm(``int` `n)``{``    ``// Let us find roots of equation x * (x + 1)/2 = n``    ``n = n * 2;``    ``int` `a = 1, b = 1, c = -1 * n;``    ``int` `d = b * b - 4 * a * c;``    ``double` `sqrt_val = ``sqrt``(``abs``(d));``    ``int` `x1 = (``double``)(-b + sqrt_val) / (2 * a);``    ``int` `x2 = (``double``)(-b - sqrt_val) / (2 * a);`` ` `    ``if` `(x1 >= 1)``        ``cout << (``char``)(``'a'` `+ x1) << endl;``    ``else` `if` `(x2 >= 1)``        ``cout << (``char``)(``'a'` `+ x2) << endl;``}`` ` `// Driver program``int` `main()``{``    ``int` `n = 12;``    ``findNthTerm(n);`` ` `    ``n = 288;``    ``findNthTerm(n);`` ` `    ``return` `0;``}`

Java

 `// Java program to find nth``// term of the given series``import` `java.io.*;`` ` `class` `GFG {`` ` `    ``// Function to find nth term``    ``// of the given series``    ``static` `void` `findNthTerm(``int` `n)``    ``{``        ``// Let us find roots of``        ``// equation x * (x + 1)/2 = n``        ``n = n * ``2``;``        ``int` `a = ``1``, b = ``1``, c = -``1` `* n;``        ``int` `d = b * b - ``4` `* a * c;``        ``double` `sqrt_val = Math.sqrt(Math.abs(d));``        ``int` `x1 = (``int``)((-b + sqrt_val) / (``2` `* a));``        ``int` `x2 = (``int``)((-b - sqrt_val) / (``2` `* a));`` ` `        ``if` `(x1 >= ``1``)``            ``System.out.println((``char``)(``'a'` `+ x1));``        ``else` `if` `(x2 >= ``1``)``            ``System.out.println((``char``)(``'a'` `+ x2));``    ``}`` ` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``12``;``        ``findNthTerm(n);`` ` `        ``n = ``288``;``        ``findNthTerm(n);``    ``}``}`` ` `// This code has been contributed``// by anuj_67.`

Python 3

 `# Python 3 program to find nth``# term of the given series``import` `math`` ` `# Function to find nth term ``# of the given series``def` `findNthTerm(n):`` ` `    ``# Let us find roots of ``    ``# equation x * (x + 1)/2 = n``    ``n ``=` `n ``*` `2``    ``a ``=` `1``    ``b ``=` `1``    ``c ``=` `-``1` `*` `n``    ``d ``=` `b ``*` `b ``-` `4` `*` `a ``*` `c``    ``sqrt_val ``=` `math.sqrt(``abs``(d))``    ``x1 ``=` `(``-``b ``+` `sqrt_val) ``/``/` `(``2` `*` `a)``    ``x2 ``=` `(``-``b ``-` `sqrt_val) ``/``/` `(``2` `*` `a)``    ``x1 ``=` `int``(x1)``    ``x2 ``=` `int``(x2)``     ` `    ``# ASCII of 'a' is 97``    ``if` `(x1 >``=` `1``):``        ``print``(``chr``(``97``+``x1))``    ``elif` `(x2 >``=` `1``):``        ``print``(``chr``(``97``+``x2))`` ` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``n ``=` `12``    ``findNthTerm(n)`` ` `    ``n ``=` `288``    ``findNthTerm(n)`` ` `# This code is contributed``# by ChitraNayal`

C#

 `// C# program to find nth``// term of the given series``using` `System;`` ` `public` `class` `GFG {`` ` `    ``// Function to find nth term``    ``// of the given series``    ``static` `void` `findNthTerm(``int` `n)``    ``{``        ``// Let us find roots of``        ``// equation x * (x + 1)/2 = n``        ``n = n * 2;``        ``int` `a = 1, b = 1, c = -1 * n;``        ``int` `d = b * b - 4 * a * c;``        ``double` `sqrt_val = Math.Sqrt(Math.Abs(d));``        ``int` `x1 = (``int``)((-b + sqrt_val) / (2 * a));``        ``int` `x2 = (``int``)((-b - sqrt_val) / (2 * a));`` ` `        ``if` `(x1 >= 1)``            ``Console.WriteLine((``char``)(``'a'` `+ x1));``        ``else` `if` `(x2 >= 1)``            ``Console.WriteLine((``char``)(``'a'` `+ x2));``    ``}`` ` `    ``// Driver Code``    ``static` `public` `void` `Main(String[] args)``    ``{``        ``int` `n = 12;``        ``findNthTerm(n);`` ` `        ``n = 288;``        ``findNthTerm(n);``    ``}``}``// contributed by Arnab Kundu`

PHP

 `= 1)``        ``echo` `chr``(97+``\$x1``) . ``"\n"``;``    ``else` `if` `((int)``\$x2` `>= 1)``        ``echo` `chr``(97+``\$x2``), ``"\n"``;``}`` ` `// Driver Code``\$n` `= 12;``findNthTerm(``\$n``);`` ` `\$n` `= 288;``findNthTerm(``\$n``);`` ` `// This Code is contributed by mits``?>`

Javascript

 ``

Output:

```e
x```

Time complexity: O(n) // Because using inbuilt function sqrt

Auxiliary Space: O(1)

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