A caterpillar crawls up a pole 75 inches high, starting from the ground. Each day it crawls up 5 inches and each night it slides down 4 inches. When will it first reach the top of the pole?

The net progress of the caterpillar in a full 24-hour cycle (one day and one night) is:
$$5\text{inches}-4\text{inches}=1\text{inch per day}$$

However, on the final day, when it climbs $5\text{inches}$ and touches the top ($75\text{inches}$), it will not slide back down.
Let's look at its height at the end of the $70\text{th}$ night cycle:

$$\text{Height}=70\times 1=70\text{inches}$$

On the next day (the $71\text{th}$ day), it climbs up $5\text{inches}$:

$$\text{New Height}=70+5=75\text{inches}$$

Since it reaches the top of the pole on the 71st day, it accomplishes the goal before sliding down again.