Find the 5th Term 7640 , 764 , 76.4 , 7.64

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 ${\displaystyle \frac{1}{10}}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=7640}$ and ${\displaystyle r=\frac{1}{10}}$.

Apply the product rule to ${\displaystyle \frac{1}{10}}$.

One to any power is one.

Combine ${\displaystyle 7640}$ and ${\displaystyle \frac{1}{{10}^{n-1}}}$.

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