Identify the Progression 1/3 , 3/15 , 9/75 , 27/375

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by ${\displaystyle \frac{3}{5}}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=\frac{3}{5}}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=\frac{1}{3}}$ and ${\displaystyle r=\frac{3}{5}}$.

Apply the product rule to ${\displaystyle \frac{3}{5}}$.

Combine.