Question

Enter the explicit rule for the geometric sequence. 1/4, 1/2, 1, 2, 4, …

Answer 1

Answer:

$a_n = (\frac{1}{4})2^{n-1}$

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is the same, and this quotient is given by q.

The explicit rule of a geometric sequence is given by:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

1/4, 1/2, 1, 2, 4

This means that $a_1 = \frac{1}{4}$, and:

$q = \frac{4}{2} = \frac{2}{1} = \frac{1}{\frac{1}{2}} = \frac{\frac{1}{2}}{\frac{1}{4}} = 2$

So the explicit rule is:

$a_n = (\frac{1}{4})2^{n-1}$