Find the 5th Term 120 , 36 , 10.8

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 ${\displaystyle \frac{3}{10}}$ gives the next term. In other words, ${\displaystyle a_n=a_1\cdot r^{n-1}}$.

Geometric Sequence: ${\displaystyle r=\frac{3}{10}}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=120}$ and ${\displaystyle r=\frac{3}{10}}$.

Apply the product rule to ${\displaystyle \frac{3}{10}}$.

Combine ${\displaystyle 120}$ and ${\displaystyle \frac{3^{n-1}}{{10}^{n-1}}}$.

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