Question

You drop a ball from a height of 1.5 meters. Each curved path has 75% of the height of the previous path. a. Write a rule for the sequence using centimeters. The initial height is given by the term n = 1. b. What height will the ball be at the top of the sixth path?

Answer 1

150 × (.75)^x-1 for part A

the second part is:

33.3 cm's

I hope this helps!

Answer 2

a)

The rule for the sequence is given by:

`a_n=150\cdot (0.75)^(n-1)`

b)

The height of ball at the top of sixth path is:

35.5957 cm.

Explanation:

a)

Let the nth term of the sequence is represented by:

`a_n`

i.e. it represent the height of the ball in nth path.

It is given that:

You drop a ball from a height of 1.5 meters.

This means that the initial height of the ball is: 1.5 meters

We know that 1 meter= 100 centimeter(cm)

This means that:

1.5 meter= 150 cm.

Hence, we have:
`a_1=150`

Also, Each curved path has 75% of the height of the previous path.

This means that:

`a_2=(0.75)\cdot a_1`

`a_3=(0.75)\cdot a_2=(0.75)^2\cdot a_1`

`a_4=(0.75)\cdot a_3=(0.75)^3\cdot a_1`

and so on.

Hence, we may write the nth term in general form by:

`a_n=(0.75)^(n-1)\cdot 150`

b)

The height of the ball at the top of sixth path.

i.e. the value of
`a_n` when n=6 is:

`a_6=(0.75)^(6-1)\cdot 150\\\\i.e.\\\\a_6=(0.75)^5\cdot 150\\\\i.e.\\\\a_6=35.5957\ \text{cm}`