# Please can you help?

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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.

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

9 days

#### Explanation:

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:

So, on an average you might think that it will take

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.