Find the Next Term 3/5 , 1/5 , 1/15 , 1/45

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 ${\displaystyle \frac{1}{3}}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=\frac{1}{3}}$

This is the form of a geometric sequence.

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

Apply the product rule to ${\displaystyle \frac{1}{3}}$.

Combine.

One to any power is one.

Multiply ${\displaystyle 3}$ by ${\displaystyle 1}$.

Substitute in the value of ${\displaystyle n}$ to find the ${\displaystyle n}$th term.