Question

Help, I'm bad at math!

Answer 1

A bouncing ball issue reaches its next peak as some fraction or multiple of the previous peak, so, that'd make it a geometric sequence.

so, let's take a peek, 27, 18, 12

now, to get the common factor from a geometric sequence, since it's just a multiplier, if you divide any of the terms by the term before it, the quotient is then the common factor, let's do so with hmm say 12 and 18, 12/18 = 2/3  <---- the common factor, you can check if you so wish with 18/27.

and the first term is of course, 27.

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=27\\ r=\frac{2}{3} \end{cases}\implies a_n=27\left( \frac{2}{3} \right)^{n-1}$