Question

What is the explicit rule for the geometric sequence? 25.5, 5.1, 1.02, 0.204, ... an=25.5(15)n an=25.5(15)n−1 an=25.5(15)n+1 an=25.5(15)n+2

Answer 1

Given:

The geometric sequence is:

25.5, 5.1, 1.02, 0.204, ...

To find:

The explicit rule for the given geometric sequence.

Solution:

We have,

25.5, 5.1, 1.02, 0.204, ...

Here, the first term is 25.5 and the common ratio is:

$r=\dfrac{a_2}{a_1}$

$r=\dfrac{5.1}{25.5}$

$r=\dfrac{1}{5}$

The explicit rule for a geometric sequence is:

$a_n=ar^{n-1}$

Where, a is the first term and r is the common ratio.

Putting $a=25.5,\ r=\dfrac{1}{5}$ in the above formula, we get

$a_n=25.5(\dfrac{1}{5})^{n-1}$

Therefore, the correct option is B.