Introduction :

 

A pentagonal number is  the  figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons whose sides contain 1 to n dots, overlaid so that they share one vertex.

 

The pentagonal numbers are number of a pentagon .It can be denoted as 1, 5, 12,22 .

 

 

Formula and diagramatic form of pentagonal number

 

Pentagonal number diagram:

 

It can be denoted as 1, 5, 12,22 ,34 in below

                

The formula to find the nth pentagonal number is

                           n( 3n – 1)
                         _______________
                                   2

 Now we see about worked examples in pentagonal number.

 

Problems in pentagonal number

 

 Example 1:  Find the  4th  pentagonal number

 

                                                                  4 x (3.4 – 1)
  By using the above formula we get:           ____________  
                                                                            2

                                                               =  2 x 11  = 22

 The 4th pentagonal number is 22

 Example 2:  Find the  18th  pentagonal number

                                                        18 x (3.18 – 1)
By using the above formula we get:         ____________  
                                                                  2

                                                        =  9 x 51  = 459

 The 18th pentagonal number is 459

Example 3:  Find the  20th  pentagonal number

                                                 20 x (3.20 – 1)
By using the above formula we get:  ____________  
                                                        2

                                                               =  10 x 57  = 570

The 20th pentagonal number  is 570

Example 4:  Find the  16th  pentagonal number

                                                          16 x (3.16 – 1)
       By using the above formula we get:     ____________  
                                                                      2

                                                      =  8 x 45  = 360

The 16th pentagonal number  is 360

Example 5:  Find the  14th  pentagonal number

                                                           14 x (3.14 – 1)
       By using the above formula we get: ____________  
                                                                  2

                                                               =  7 x 13  = 39

The 14th pentagonal number is 39

Example 6:  Find the  12th  pentagonal number

                                                           12 x (3.12 – 1)
       By using the above formula we get:     ____________  
                                                                   2

                                                                = 6 x 33 = 198

The 12th pentagonal number  in 198

 

Between, if you have problem on these topics Divisibility Rules for 11, please browse expert math related websites for more help on sample papers for 12 cbse.

 

Example 7:  Find the  10th  pentagonal number

                                                          10 x (3.10 – 1)
       By using the above formula we get:     ____________  
                                                                  2

                                                               = 5 x 27 = 135

The 10th pentagonal number is 135

Example 8:  Find the  8th  pentagonal number

                                                          8 x (3.8 – 1)
       By using the above formula we get: ____________ 
                                                                     2

                                                               =  4 x 7  = 28

The     8th pentagonal number  is 28

 

Example 8:  Find the  8th  pentagonal number

 

                                                 8 x (3.8 – 1)

By using the above formula we get: ____________  

                                                     2

                                            =  4 x 7  = 28

 

The     8th pentagonal number  is 28