A ball is dropped from a height of 5m. After each bounce it rises to 35% of its previous height. After how many bounces does the ball reach a Height of less than 50cm?

After the third bounce the ball reaches a height of less than 50cm.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, and it's called common ratio. The nth term of a geometric sequence is given by:

In which is the first term and r is the common ratio.

A ball is dropped from a height of 5m.

This means that

After each bounce it rises to 35% of its previous height.

This means that

Thus

After how many bounces does the ball reach a Height of less than 50cm?

50cm = 0.5m. This is n for which . Thus

Rounding up:

After the third bounce the ball reaches a height of less than 50cm.

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step-by-step explanation: