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Write-up


Title
Pascal Triangle
 

Problem Statement
 What is the sum of each row?

Row #                Sum

1                   1=1
2                   1x2= 2         
3                   2x2= 4         
4                   4x2= 8         
5                   8x2= 16       
6                   16x2= 32     
7                   32x2= 64    
8                   64x2= 128   
9                   128x2= 256   
10                 256x2= 512   

 

Describe the pattern of the sums.

Compare each row's sum to the corresponding row number

Problem setup

How is the sum of each row determined?

You double the sum of the previous row.

 

Plans to Solve/Investigate the Problem

 

The sum of each sequential row is doubled this is called a geometric sequence.

 

 

Investigation/Exploration of the Problem

                1  
              1   1              
            1   2   1            
          1   3   3   1          
        1   4   6   4   1        
      1   5   10   10   5   1      
    1   6   15   20   15   6   1    
  1   7   21   35   35   21   7   1  
1   8   28   56   70   56   28   8   1

 

Row #                Sum

1                   1=1
2                   1x2= 2          or      21
3                   2x2= 4          or      22
4                   4x2= 8          or     23
5                   8x2= 16        or     24
6                   16x2= 32      or     25
7                   32x2= 64      or     26
8                   64x2= 128    or     27
9                   128x2= 256  or     28
10                 256x2= 512  or     29