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

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, …..Want to learn from the best curated videos and practice problems, check out theC++ Foundation Coursefor Basic to Advanced C++ andC++ STL Coursefor the language and STL. To complete your preparation from learning a language to DS Algo and many more, please referComplete Interview Preparation Course.

**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 <bits/stdc++.h>` `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

`<?php` `// PHP program to find nth` `// term of the given series` `// Function to find nth term` `// of the given series` `function` `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` `;` ` ` `$sqrt_val` `= sqrt(` `abs` `(` `$d` `));` ` ` `$x1` `= (-` `$b` `+ ` `$sqrt_val` `) / (2 * ` `$a` `);` ` ` `$x2` `= (-` `$b` `- ` `$sqrt_val` `) / (2 * ` `$a` `);` ` ` `// Ascii of 'a' is 97` ` ` `if` `((int)` `$x1` `>= 1)` ` ` `echo` `chr` `(97+` `$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

`<script>` `// Javascript program to find nth` `// term of the given series` `const str = ` `"abcdefghijklmnopqrstuvwxyz"` `;` `// Function to find nth term` ` ` `// of the given series` ` ` `function` `findNthTerm( n) {` ` ` `// Let us find roots of` ` ` `// equation x * (x + 1)/2 = n` ` ` `n = n * 2;` ` ` `let a = 1, b = 1, c = -1 * n;` ` ` `let d = b * b - 4 * a * c;` ` ` `let sqrt_val = Math.sqrt(Math.abs(d));` ` ` `let x1 = parseInt( ((-b + sqrt_val) / (2 * a)));` ` ` `let x2 = parseInt( ((-b - sqrt_val) / (2 * a)));` ` ` `if` `(x1 >= 1)` ` ` `document.write(str[x1]+` `"<br/>"` `);` ` ` `else` `if` `(x2 >= 1)` ` ` `document.write(str[x2]+` `"<br/>"` `);` ` ` `}` ` ` `// Driver Code` ` ` ` ` `let n = 12;` ` ` `findNthTerm(n);` ` ` `n = 288;` ` ` `findNthTerm(n);` `// This code is contributed by shikhasingrajput` `</script>` |

**Output:**

e x