Find the Next Term 1 , 4 , 16 , 64 , 256

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 ${\displaystyle 4}$ 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 ${\displaystyle a_1=1}$ and ${\displaystyle r=4}$.

Multiply ${\displaystyle 4^{n-1}}$ by ${\displaystyle 1}$.

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

Subtract ${\displaystyle 1}$ from ${\displaystyle 6}$.