You drop a ball from a height of 0.5 meter. Each curved path has 52% 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 third path?



4 years ago Comment

This is a geometric sequence.  The first term is the max height of the first curved path, which is 0.5.  The second one is 52% of that meaning that it is 0.52 times the first term.  The third term is 0.52 times the second term. Thus, in this geometric sequence,

[latex]a = 0.5 [/latex]
[latex]r = 0.52 [/latex]

You will need to use the relation [latex] a_n = a \cdot r^{n-1} [/latex]