A frog is at the bottom of a 17-foot well. Each time the frog leaps, it moves up 3 feet. If the frog has not reached the top of the well, then the frog slides back 1 foot before it is ready to make another leap. How many leaps will the frog need to escape the well?

The frog takes 8 jumps to reach top of well

Explanation:

Given data

Frog at bottom=17 foot

Each time frog leaps 3 feet

Frog has not reached the top of the well, then the frog slides back 1 foot

To Find

Total number of leaps the frog needed to escape from well

Solution

in 1 jump distance jumped=3 + (-1)

=2 feet

=2*1 feet

The "-1" is because the frog goes back

Now After 2 jumps the distance jumped as:

Distance Jumped=2+2

Distance Jumped=2*2

=4 feet

Similarly after 7 jumps

Distance Jumped=2+2 + ... + 2

Distance Jumped=2*7

=14 feet

Now after 8th jump the frog climbs but doesnot slide back as it is reached to the top of well.

So

Distance Jumped = (Distance Jumped after 7 jumps) + 3

=14+3

=17 feet

The frog takes 8 jumps to reach top of well