The pentagonal numbers

Rule

Each term is: 3/2 times the number squared minus 1/2 times the number

Known as: The pentagonal numbers

The first 50 terms (starting from n=1) are:

1 5 12 22 35 51 70 92 117 145 176 210 247 287 330 376 425 477 532 590 651 715 782 852 925 1001 1080 1162 1247 1335 1426 1520 1617 1717 1820 1926 2035 2147 2262 2380 2501 2625 2752 2882 3015 3151 3290 3432 3577 3725

Example

To get the value for n=13:

• Take 3/2 times the number squared, giving 507/2
• Subtract 1/2 times the number, giving 247

So the result is 247.