Please can you help?

A snail climbs 6 m up a well during the day and slides down 4 m at night while its sleeping.
a) Describe a sequence that represents the height of the snail.
b) If the well is 20 m deep how many days does it take the snail to climb up from the bottom of the well.

1 Answer
Jun 16, 2018

9 days


The sequence graphed against time would look like an increasing saw-toothed ramp.

The NET progress is just the advance less the decline each day:
#6 - 4 = 2#m per day.
So, on an average you might think that it will take #20/2 = 10# days to climb out.
HOWEVER, because the "average" is taken at the completion of each cycle, but the increase occurs first , it only needs to get to within 6 meters of the edge to get out in the current cycle. This occurs at the beginning of Day 8, so the snail gets OUT at the end of Day 9.