Mathematics GCSE Coursework - Patterns with Fractions.

2)

3)

4)

5)

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8)

9)

Patterns.

The first pattern that I saw was that the horizontal line 2) this is the same as the first diagonal line on the left (starting , , ). This carries on going-the third horizontal line is the same as the second diagonal line.

Another pattern which only works on line 1) to find the denominator of the difference is n*(n+1) e.g. to find the difference between and is 3*4=12 so the difference between them is

Equations.

For the first line the equation is

I have found an equation that lets you find out the next denominator.

P+() In this equation x is the horizontal line down (in this the first line is , , etc) and P is the previous denominator in the sequence, and n is the number in the sequence.

Another equation was (for the second line)

For the third line

Forth