Question

find the common ratio, 5/12, 1/3, 4/15, 16/75, 64/375

Answer 1

\[\left\{\left\{\frac{5}{12}/\frac{1}{3}\right\},\left\{\frac{1}{3}/\frac{4}{15}\right\},\left\{\frac{4}{15}/\frac{16}{75}\right\},\left\{\frac{16}{75}/\frac{64}{375}\right\}\right\}\to \]\[\left\{\left\{\frac{5}{4}\right\},\left\{\frac{5}{4}\right\},\left\{\frac{5}{4}\right\},\left\{\frac{5}{4}\right\}\right\} \]

Answer 2

\[
a_1= \frac 5 {12}\\
a_n= \frac 4 5 a_{n-1}
\]