PHP program to find if a number is present in a given sequence of numbers

In PHP, you can check if a specific number exists in an arithmetic sequence by comparing the target number with the sequence parameters. This involves checking if the number can be reached by adding a common difference repeatedly to a starting number.

Example

The following code demonstrates how to find if a number is present in a given arithmetic sequence −

<?php
function contains_in_sequence($start, $target, $step)
{
    if ($start == $target)
        return true;
    
    if (($target - $start) * $step > 0 &&
        ($target - $start) % $step == 0)
        return true;
    
    return false;
}

$start = 11; 
$target = 99; 
$step = 2;

print_r("Is the number present in the sequence? ");
if (contains_in_sequence($start, $target, $step))
    echo "Yes, it is present in the sequence";
else
    echo "No, it is not present in the sequence";
?>

Is the number present in the sequence? Yes, it is present in the sequence

How It Works

The contains_in_sequence() function checks if a target number exists in an arithmetic sequence by:

• First checking if the target equals the starting number
• Then verifying if the difference between target and start is divisible by the step size
• Ensuring the step direction matches (positive or negative difference)

In this example, the sequence starts at 11 with a step of 2, generating: 11, 13, 15, 17, ..., 97, 99. Since 99 can be reached from 11 by adding 2 repeatedly (44 times), the function returns true.

Conclusion

This method efficiently determines if a number exists in an arithmetic sequence using mathematical properties rather than iterating through all sequence values. It works for both increasing and decreasing sequences.