PHP Program to Find Sum of n Natural Numbers

You can find the sum of n natural numbers in PHP using the formula $sum = $n * ($n + 1) / 2; or by looping from 1 to n and adding each number.

Examples

Input5

OutputSum of first 5 natural numbers is 15

Input10

OutputSum of first 10 natural numbers is 55

Input1

OutputSum of first 1 natural number is 1

How to Think About It

To find the sum of n natural numbers, think of adding all numbers from 1 up to n. You can do this by adding each number one by one or use a simple math formula that calculates the total quickly without adding each number.

Algorithm

1

Get the input number n from the user.

2

Calculate the sum using the formula sum = n * (n + 1) / 2.

3

Print the result.

Code

php

<?php
$n = 10; // You can change this value
$sum = $n * ($n + 1) / 2;
echo "Sum of first $n natural numbers is $sum";
?>

Output

Sum of first 10 natural numbers is 55

Dry Run

Let's trace the example where n = 5 through the code

1

Set n

$n = 5

2

Calculate sum

$sum = 5 * (5 + 1) / 2 = 5 * 6 / 2 = 30 / 2 = 15

3

Print result

Output: Sum of first 5 natural numbers is 15

n	Calculation	Sum
5	5 * (5 + 1) / 2	15

Why This Works

Step 1: Using the formula

The formula n * (n + 1) / 2 quickly calculates the sum of numbers from 1 to n without looping.

Step 2: Multiplication and division

First multiply n by (n + 1), then divide the result by 2 to get the sum.

Step 3: Output the result

Print the sum with a clear message so the user understands the output.

Alternative Approaches

Using a for loop

php

<?php
$n = 10;
$sum = 0;
for ($i = 1; $i <= $n; $i++) {
    $sum += $i;
}
echo "Sum of first $n natural numbers is $sum";
?>

This method uses a loop to add each number one by one, which is easy to understand but slower for large n.

Using recursion

php

<?php
function sumNatural($n) {
    if ($n == 1) return 1;
    return $n + sumNatural($n - 1);
}
$n = 10;
echo "Sum of first $n natural numbers is " . sumNatural($n);
?>

Recursion calls the function repeatedly but can be less efficient and harder for beginners.

Complexity: O(1) time, O(1) space

Time Complexity

Using the formula takes constant time because it does a fixed number of operations regardless of n.

Space Complexity

The formula uses only a few variables, so it requires constant space.

Which Approach is Fastest?

The formula approach is fastest and most efficient compared to looping or recursion.

Approach	Time	Space	Best For
Formula	O(1)	O(1)	Fastest and simplest for any n
For Loop	O(n)	O(1)	Easy to understand, good for small n
Recursion	O(n)	O(n)	Demonstrates recursion, less efficient