Answer:
[tex]a_n = 2( \frac{1}{2})^{n - 1} [/tex]
Step-by-step explanation:
The given pattern is:
[tex]2,1, \frac{1}{2} , \frac{1}{4} [/tex]
The first term is
[tex]a_1=2[/tex]
The common ratio is the previous term of any consecutive two terms over the previous term.
[tex]r = \frac{1}{2} [/tex]
The explicit formula that describes this pattern is:
[tex]a_n = a_1 {r}^{n - 1} [/tex]
We substitute the common ratio and the first term to get:
[tex]a_n = 2( \frac{1}{2} )^{n - 1} [/tex]
