The Fibonacci sequence is a sequence of numbers in which each number is the sum of the two preceding numbers. It is named after Leonardo of Pisa, who was known as Fibonacci, and was introduced to the Western world in his book “Liber Abaci” published in 1202. The Fibonacci sequence has many interesting properties and appears in various areas of mathematics and science.

```
<?php
// Define the number of terms in the sequence
$terms = 10;
// Initialize the first two terms
$first = 0;
$second = 1;
// Output the first two terms
echo $first . " " . $second . " ";
// Loop through the remaining terms
for ($i = 2; $i < $terms; $i++) {
// Calculate the next term
$next = $first + $second;
// Output the next term
echo $next . " ";
// Shift the terms for the next iteration
$first = $second;
$second = $next;
}
```

In this code, we first define the number of terms in the sequence using the `$terms`

variable. We then initialize two variables, `$first`

and `$second`

, to store the first two terms of the sequence.

Next, we use a `for`

loop to iterate through the remaining terms in the sequence. In each iteration, we calculate the next term by summing the current `$first`

and `$second`

terms. We then output the next term using the `echo`

statement, and shift the terms for the next iteration.

Finally, we use the `echo`

statement to output the first two terms of the sequence, followed by the remaining terms, separated by spaces.

This simple implementation of the Fibonacci sequence in PHP demonstrates how a simple algorithm can generate a sequence of numbers with many interesting properties. It is a great example for beginners to learn about loops and basic arithmetic operations in programming.