Identify the Progression 1 , 4 , 16 , 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 ${\displaystyle 4}$ 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 ${\displaystyle r=4}$.