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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: Term (n) Numerator (n) Denominator (n + 1) Final Fraction 1 1 2 ? 2 2 3 ? 3 3 4 ? 4 4 5 ? 5 5 6 ? (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: Term (n) Numerator (1) Denominator (n + 1)(n+2) Final Fraction 1 1 (1+1)(1+2) = 6 ? 2 1 (2+1)(2+2) = 12 ? 3 1 (3+1)(3+2) = 20 ? 4 1 (4+1)(4+2) = 30 ? 5 1 (5+1)(5+2) = 42 ? (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...

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