Height of the building = x

height of third bounce = 6.75 m

Number of bounce = 3

Equation (Geometric sequence formula):

(3/4)³ (x) = 6.75

(27/64) (x) = 6.75

(64/27) [ (27/64)(x) = 6.75 ] (64/27)

x = (6.75) (64/27)

x = 432/27

x = 16

**ANSWER: The height (of the building) from which the ball was dropped**

** is 16 m.**

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Check:

To find the height of second bounce:

**6.75 = height of the 3rd bounce.**

x₂ = height of the second bounce

Since 6.75 is 3/4 of the height of the previous bounce x₂, then:

3/4 (x₂) = 6.75

(4/3) [3/4 (x₂) = 6.75 ] (4/3)

x₂ = 6.75 (4/3)

**x₂ = 9 m, height of the second bounce**

To find the height of first bounce:

9 m = height of the second bounce

x₁ = height of the first bounce

Since 9 m is 3/4 of the first bounce x₁, then:

3/4 (x₁) = 9

(4/3) [ 3/4 (x₁) = 9] (4/3)

**x₁ = 12 **,** height of the first bounce**

To find the height from where the ball was dropped:

12 m = height of the first bounce

x = height of the building

Since 12 m is 3/4 of the height from where the ball was dropped, then:

3/4 (x) = 12

(4/3) [ 3/4(x) = 12)] (4/3)

x = 12 (4/3)

**x = 16 m, the height from where the object was dropped.**