Coursework regarding fraction differences (sequence with nth term- fractions)

hi everyone!

ok, i have an investigation where i must consider some fraction sequences.

first row- 1/2, 2/3, 3/4, 4/5 5/6, 6/7, 78

second row- 1/6, 1/12, 1/20, 1/30, 1/42, 1/56

third row- 1/12, 1/30, 1/60, 1/105, 1/168

fourth- 1/20, 1/60, 1/140, 1/280

(there are 3 more rows aswell)

my task is to find out the nth term for each row(rule) and explain why the rule works algebraically.

the relationship between the rows is the first two between the fractions are that the two fractions above are minused which gives you that fraction.(it becomes obvious when you look.)

i have figured out the rule for the first row--- n/(n+1)

i just looked and could see that the numerator was exactly the same as n, and the denominator was n+1.

and thats all i have done.

i dont know how to figure out the rest, if anyone out there knows then that would be very much appriciated!

cheers

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