A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right. The n-th triangular number is the number of dots composing a triangle with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n.
Examples :
Input : 5 Output : 1 3 6 10 15 Input : 10 Output : 1 3 6 10 15 21 28 36 45 55 Explanation : For k = 1 and j = 1 -> print k ( i.e. 1); increase j by 1 and add into k then print k ( i.e 3 ) update k increase j by 1 and add into k then print k ( i.e 6 ) update k increase j by 1 and add into k then print k ( i.e 10 ) update k increase j by 1 and add into k then print k ( i.e 15 ) update k increase j by 1 and add into k then print k ( i.e 21 ) update k . . and so on.
Approach used is very simple. Iterate for loop till the value given n and for each iteration increase j by 1 and add it into k, which will simply print the triangular number series till n.
Below is the program implementing above approach:
// C++ Program to find Triangular Number Series #include <iostream> using namespace std;
// Function to find triangular number void triangular_series( int n)
{ int i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++) {
cout << k << " " ;
j = j + 1; // Increasing j by 1
k = k + j; // Add value of j into k and update k
}
} // Driven Function int main()
{ int n = 5;
triangular_series(n);
return 0;
} //this code is contributed by aditya942003patil |
// C Program to find Triangular Number Series #include <stdio.h> // Function to find triangular number void triangular_series( int n)
{ int i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++) {
printf ( " %d " , k);
j = j + 1; // Increasing j by 1
k = k + j; // Add value of j into k and update k
}
} // Driven Function int main()
{ int n = 5;
triangular_series(n);
return 0;
} |
// Java Program to print triangular number series till n import java.util.*;
class GFG {
// Function to find triangular number
static void triangular_series( int n)
{
int i, j = 1 , k = 1 ;
// For each iteration increase j by 1
// and add it into k
for (i = 1 ; i <= n; i++) {
System.out.printf( "%d " , k);
j = j + 1 ; // Increasing j by 1
k = k + j; // Add value of j into k and update k
}
}
// Driver function
public static void main(String[] args)
{
int n = 5 ;
triangular_series(n);
}
} // This code is contributed by Arnav Kr. Mandal. |
# Python3 code to find Triangular # Number Series # Function to find triangular number def triangular_series( n ):
j = 1
k = 1
# For each iteration increase j
# by 1 and add it into k
for i in range ( 1 , n + 1 ):
print (k, end = ' ' )
j = j + 1 # Increasing j by 1
# Add value of j into k and update k
k = k + j
# Driven Code n = 5
triangular_series(n) # This code is contributed by "Sharad_Bhardwaj" |
// C# Program to print triangular // number series till n using System;
class GFG {
// Function to find triangular number
static void triangular_series( int n)
{
int i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++) {
Console.Write(k + " " );
j += 1; // Increasing j by 1
k += j; // Add value of j into k and update k
}
}
// Driver Code
public static void Main()
{
int n = 5;
triangular_series(n);
}
} // This code is contributed by vt_m. |
<?php // PHP Program to find // Triangular Number Series // Function to find // triangular number function triangular_series( $n )
{ $i ; $j = 1; $k = 1;
// For each iteration increase j
// by 1 and add it into k
for ( $i = 1; $i <= $n ; $i ++)
{
echo ( " " . $k . " " );
// Increasing j by 1
$j = $j + 1;
// Add value of j into k and update k
$k = $k + $j ;
}
} // Driver Code $n = 5;
triangular_series( $n );
// This code is contributed by Ajit. ?> |
<script> // javascript Program to find Triangular Number Series // Function to find triangular number function triangular_series( n)
{ let i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++)
{
document.write(k+ " " );
j = j + 1; // Increasing j by 1
k = k + j; // Add value of j into k and update k
}
} // Driven Function let n = 5;
triangular_series(n);
// This code is contributed by Rajput-Ji </script> |
Output :
1 3 6 10 15
Time complexity : O(n)
Auxiliary Space : O(1), since no extra space has been taken.
Alternate Solution :
The solution is based on the fact that i-th Triangular number is sum of first i natural numbers, i.e., i * (i + 1)/2
// C++ Program to find Triangular Number Series #include <iostream> using namespace std;
// Function to find triangular number void triangular_series( int n)
{ for ( int i = 1; i <= n; i++)
cout << i*(i+1)/2 << " " ;
} // Driven Function int main()
{ int n = 5;
triangular_series(n);
return 0;
} //this code is contributed by aditya942003patil |
// C Program to find Triangular Number Series #include <stdio.h> // Function to find triangular number void triangular_series( int n)
{ for ( int i = 1; i <= n; i++)
printf ( " %d " , i*(i+1)/2);
} // Driven Function int main()
{ int n = 5;
triangular_series(n);
return 0;
} |
//Java program to print triangular number series till n import java.util.*;
class GFG {
// Function to find triangular number
static void triangular_series( int n)
{
for ( int i = 1 ; i <= n; i++)
System.out.printf( "%d " ;, i*(i+ 1 )/ 2 );
}
// Driver function
public static void main(String[] args)
{
int n = 5 ;
triangular_series(n);
}
} //This code is contributed by Arnav Kr. Mandal. |
# Python3 code to find Triangular # Number Series def triangular_series(n):
for i in range ( 1 , n + 1 ):
print ( i * (i + 1 ) / / 2 ,end = ' ' )
# Driver code n = 5
triangular_series(n) # This code is contributed by ihritik |
// C# program to print triangular // number series till n using System;
class GFG {
// Function to find triangular number
static void triangular_series( int n)
{
for ( int i = 1; i <= n; i++)
Console.Write(i * (i + 1) / 2 + " " );
}
// Driver Code
public static void Main()
{
int n = 5;
triangular_series(n);
}
} // This code is contributed by vt_m. |
<?php // PHP Program to find // Triangular Number Series // Function to find // triangular number function triangular_series( $n )
{ for ( $i = 1; $i <= $n ; $i ++)
echo ( " " . $i * ( $i + 1) /
2 . " " );
} // Driver Code $n = 5;
triangular_series( $n );
// This code is contributed by Ajit. ?> |
<script> // javascript Program to find Triangular Number Series // Function to find triangular number function triangular_series( n)
{ for (let i = 1; i <= n; i++)
document.write( " " + i * (i + 1)/2);
} // Driven Function let n = 5;
triangular_series(n);
// This code is contributed by gauravrajput1
</script> |
Output :
1 3 6 10 15
Time complexity : O(n)
Auxiliary Space : O(1) , since no extra space has been taken.