Jack, jill and bill each carried a 48-ounce bucket full of water down the hill. by the time they reached the bottom, jack's bucket was only 3/4 full, jill's was 2/3 full, and bill's was 1/6 full. how much water did they spill altogether on their way down the hill?

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb