# How do you find the nth term rule for 1,2,4,8,16,32,64?

${2}^{n - 1}$
The formula for n th term of a geometric sequence is $a {r}^{n - 1}$ where a is the first term and r is the common ratio. In the given sequence first term is 1 and the common ratio is 2. Hence nth term would be ${2}^{n - 1}$
Note that $r = \left(\text{a term")/("previous term}\right) = \frac{2}{1} = \frac{4}{2} = \frac{8}{4} = \frac{16}{8} = 2$