Pentagonal numbers are numbers that form a pentagon shape. The nth pentagonal number can be calculated using the formula n(3n-1)/2. Some properties of pentagonal numbers include: 1) The difference between successive pentagonal numbers is 3n-2. 2) Adding successive pentagonal numbers gives the formula 3n^2 - 4n + 2. 3) Examples are provided to demonstrate calculating individual pentagonal numbers and using the properties above.

1. ADELA MUSCALU and DUMITRU ROSSE-MARYE

2. DEFINITION:
Pentagonal Numbers are numbers that create a
pentagon.
Ex. 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176 etc.

4. The nth pentagonal number can be found by
the formula:
n(3n - 1)
2
Exemple: n=5 => 5(3x5-1):2=
5x14:2=70:2=35
n=10=> 10(3x10-1):2
10x29:2=290:2=145

5. In number sense, the question will only ask
for the nth pentagonal number.
 Exemple:
8( 3x8 -1) :2=
8x23:2= 184:2=92
2. The 13th pentagonal number is:
13(3x13-1):2=
13x38:2=494:2=247
1.The 8th pentagonal number is:

6. Here are some ways of manipulating
pentagonal numbers:
 1 The difference of successive pentagonal numbers is:
3n - 2, where n is the largest
The 8th - the 9th = 3x9-2= 27-2=25
The 18th -the 19th =3x19-2=57-2=55
 2 Adding successive pentagonal numbers gives:
3n2 - 4n + 2, where n is the largest
The 8th + the 9th = 3x92 -4x9+2=243-36+2=207+2=209
The 18th + the 19th =3x192 -4x19+2=1083-76+2=1007+2=1009