Step-by-step explanation:
she painted half of the still to be painted area.
after the first weekend there were 800 of 1600 ft² painted, and therefore 1600 - 800 = 800 ft² left to be painted.
on the second weekend she then painted half of that :
800 / 2.
that means she painted 800/2 = 400 ft², and that left 800 - 400 = 400 ft² to be painted on the following weekends.
if we look in detail, we find the starting 800 ft² of the second weekend are already the result of the first weekend.
800 = 1600 / 2
so,
800 / 2 = 1600 / 2 / 2 = 1600 / 2² = 1600 / 4.
and the same principle goes on weekend after weekend.
therefore, the expression for the nth weekend could be
1600 × (1/2)^n ft²
that means, she painted
on the 1st weekend : 1600 × 1/2 = 800 ft²
on the 2nd weekend : 1600 × 1/4 = 400 ft²
on the 3rd weekend : 1600 × 1/8 = 200 ft²
on the 4th weekend : 1600 × 1/16 = 100 ft²
...
that also means : she will never be finished, as she always paints only half of what is still left open, and that leaves always some part open. it will be tinier and tinier over time, but never 0.
