# Robson » Little Red Book » Triangular numbers

## Chapter 3 - Question 8

The numbers 1, 3, 6, 10 are called triangular.

```
.
.       . .
.     . .     . . .
.   . .   . . .   . . . .
1    3      6        10
```

Write a program to generate all the triangular numbers less than 1000.

### Solution 1

`<?`
`    // start the sequence at 1`
`    \$numbers[] = 1;`
`    // loop if last generated triangular number is less than 1000`
`    while (array_sum(\$numbers) < 1000)`
`    {`
`        // add the sum of all numbers in the array to the triangular sequence`
`        \$triangular[] = array_sum(\$numbers);`
`        // add the last number plus one,`
`        // so the array will look like this after six loops:`
`        // 1, 2, 3, 4, 5, 6`
`        \$numbers[] = \$numbers[count(\$numbers)-1]+1;        `
`    }`
`    // output the sequence`
`    echo implode(', ', \$triangular);`
`?>`

Which produces:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990

## Log

• March 27, 2005 - Added solution 1.
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