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Find the sequence number of a triangular number
  • Last Updated : 17 Mar, 2021
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Given an integer N print the sequence number of the given Triangular Number. If the number is not a triangular number then print -1.
 

A number is termed as a triangular number if we can represent it in the form of a triangular grid of points such that the points form an equilateral triangle and each row contains as many points as the row number, i.e., the first row has one point, the second row has two points, the third row has three points and so on. 
First 10 tringular number are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. 
 

 

Examples: 
 



Input: N = 21 
Output:
Explanation: 
Since 15 is a 6th Tringular Number.
Input: N = 12 
Output:-1 
Explanation: 
Since 12 is not a tringular Number 
 

 

Approach: 
 

  1. Since tringular numbers are sum of natural numbers so can be generalise as quadratic equation.

 

C++




// C++ code to print sequence
// number of a triangular number
#include<bits/stdc++.h>
using namespace std;
 
int main()
{
    int N = 21;
    int A = sqrt(2 * N + 0.25) - 0.5;
    int B = A;
 
    // If N is not tringular number
    if (B != A)
        cout << "-1";
    else
        cout << B;
}
 
// This code is contributed by yatinagg

Java




// Java code to print sequence
// number of a triangular number
import java.util.*;
class GFG{
     
public static void main(String args[])
{
    int N = 21;
    int A = (int)(Math.sqrt(2 * N + 0.25) - 0.5);
    int B = A;
 
    // If N is not tringular number
    if (B != A)
        System.out.print("-1");
    else
        System.out.print(B);
}
}
 
// This code is contributed by Akanksha_Rai

Python3




# Python3 code to print sequence
# number of a triangular number
 
import math
 
N = 21
A = math.sqrt(2 * N + 0.25)-0.5
B = int(A)
 
# if N is not tringular number
if B != A:
    print(-1)
else:
    print(B)        

C#




// C# code to print sequence
// number of a triangular number
using System;
class GFG{
     
public static void Main()
{
    int N = 21;
    int A = (int)(Math.Sqrt(2 * N + 0.25) - 0.5);
    int B = A;
 
    // If N is not tringular number
    if (B != A)
        Console.Write("-1");
    else
        Console.Write(B);
}
}
 
// This code is contributed by Code_Mech

Javascript




<script>
// javascript code to print sequence
// number of a triangular number
    let N = 21;
    let A = Math.sqrt(2 * N + 0.25) - 0.5;
    let B = A;
 
    // If N is not tringular number
    if (B != A)
         document.write("-1");
    else
         document.write(B);
          
// This code is contributed by Rajput-Ji
 
</script>
Output: 
6

 

Time Complexity: O(1) 
Auxiliary Space: O(1)
 

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