Question

Which answer describes the pattern in this sequence? 2,1,12,14,...

Answer 1

Answer:

$a_n = 2( \frac{1}{2})^{n - 1}$

Step-by-step explanation:

The given pattern is:

$2,1, \frac{1}{2} , \frac{1}{4}$

The first term is

$a_1=2$

The common ratio is the previous term of any consecutive two terms over the previous term.

$r = \frac{1}{2}$

The explicit formula that describes this pattern is:

$a_n = a_1 {r}^{n - 1}$

We substitute the common ratio and the first term to get:

$a_n = 2( \frac{1}{2} )^{n - 1}$