Patterns With Fractions Investigations

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Ahzaz Chowdhury 11H

Fractions Coursework.

Mathematics Coursework.

Patterns With Fractions.

Consider the sequence of fractions and the differences between the fractions:

Term (n)          1                    2                    3                    4                    5

                                                                           

 

1st Difference                                                                       

2nd Difference                                                       

(For rest of differences, see page11)

Finding the starting fraction for the nth term:

, , , ,      =       (The general formula)

                        

Check if correct formula:

(Check On Page 11)

Finding the nth term for the 1st difference:

In order to find out the nth term for the 1st differences, the requirement is to subtract the 2nd fraction from the 1st fraction (the smaller fraction from the bigger fraction).

  -  

=                 

=                

=                  (The general formula for 1st difference)

Check if correct formula:

(Check On Page 11)

Finding the nth term for the 2nd difference:

In order to find out the nth term for the 2nd differences, the requirement is to subtract the 1st fraction from the 2nd fraction (the smaller fraction from the bigger fraction) of the 1st differences.

  -  

=                

=                   (The general formula for 2nd difference)

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Check if correct formula:

(Check On Page 11)

Finding the nth term for the 3rd difference:

In order to find out the nth term for the 3rd differences, the requirement is to subtract the 1st fraction from the 2nd fraction (the smaller fraction from the bigger fraction) of the 2nd differences.

  -  

=        

=        

=           (The general formula for 3rd difference)

Check if correct formula:

(Check On Page 11)

Finding the nth term for the 4th difference:

In order to find out the nth term for the 4th differences, the requirement ...

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