Question

A basketball has a rebound ratio of 0.8. If you drop the basketball from a heigh of 10cm, what will the height of the 5th bounce be?

Answer 1

$\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} r=0.8\\ a_1=10\\ n=5 \end{cases} \\\\\\ a_5=10(0.8)^{5-1}\implies a_5=10(0.8)^4\implies a_5=4.096$