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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?

Verified Answer :

lake356333

A(n) =150 X (o.75)^n-1; 35.6cm

Answer: The height of the ball would be 0.355 meters at the top of the sixth path.

Step-by-step explanation:

Since we have given that

Initial height  = 1.5 meters

Rate of growth = 75%

So, we need to find the height at n paths.

Since it forms geometric progression.

Here, a = 1.5

r = 0.75

So, nth term becomes

\(a_n=1.5(0.75)^{n-1}\)

We need to find the height at the top pf the sixth path.

So, it becomes,

\(a_6=1.5(0.75)^{6-1}=1.5(0.75)^5=0.355\ meters\)

Hence, the height of the ball would be 0.355 meters at the top of the sixth path.

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