Increasing Number Triangle Using $i + $j - 1 in PHP

What You’ll Learn

The increasing number triangle using $i + $j - 1 prints 1, 2 3, 3 4 5, … — a natural follow-up after Program 32’s triangle starting from 11. This tutorial covers the $i + $j - 1 formula, nested loops, a live preview, worked PHP examples, edge cases, and complexity.

📝 Problem & Approach

Given $rows = 5, print a left-shifted increasing triangle: for each row $i, print $j = 1..$i values of $i + $j - 1 separated by spaces.

// $rows = 5 (conceptual shape)
// 1
// 2 3
// 3 4 5
// 4 5 6 7
// 5 6 7 8 9

Inputs & Outputs

Minimal workflow

for i from 1 to rows:
    for j from 1 to i:
        print ($i + $j - 1) + space
    print newline

Approach comparison

🔮 Live Preview

Choose a row count between 3 and 9 and draw the increasing triangle in the browser.

Press "Draw pattern".

Examples Gallery

Three complete PHP programs — fixed rows, user input, and a smaller trace demo. Click View Output to reveal sample console results.

<?php
for ($i = 1; $i <= 5; $i++) {
    for ($j = 1; $j <= $i; $j++) {
        echo ($i + $j - 1) . " ";
    }
    echo PHP_EOL;
}

1
2 3
3 4 5
4 5 6 7
5 6 7 8 9

<?php
echo "Enter rows: ";
$rows = (int) trim(fgets(STDIN));
if ($rows < 1) return;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = 1; $j <= $i; $j++) {
        echo ($i + $j - 1) . " ";
    }
    echo PHP_EOL;
}

Enter rows: 3
1
2 3
3 4 5

<?php
$rows = 3;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = 1; $j <= $i; $j++) {
        echo ($i + $j - 1) . " ";
    }
    echo PHP_EOL;
}

1
2 3
3 4 5

🔎 Worked Walkthrough — $rows = 5

Trace each outer-loop value of $i, inner-loop range, values printed, and full row output.

Prints per row = $i — total prints = n(n+1)/2 for n rows.

🎯 Practice Problems

Try these variations to lock in the pattern.

Notes

⏱️ Time and Space Complexity

💡 Best Practices