Question

What is the explicit rule for this geometric sequence?

Answer 1

Given:

The geometric sequence is $\dfrac{2}{9},\dfrac{2}{3},2,6,...$

To find:

The explicit formula for the given geometric sequence.

Solution:

We have, a geometric sequence

$\dfrac{2}{9},\dfrac{2}{3},2,6,...$

Here,

First term : $a=\dfrac{2}{9}$

Common ratio : $r=\dfrac{\dfrac{2}{3}}{\dfrac{2}{9}}$

$r=\dfrac{2}{3}\times \dfrac{9}{2}$

$r=3$

The explicit formula of a geometric sequence is

$a_n=ar^{n-1}$

where, a is first term and r is common ratio.

Putting $a=\dfrac{2}{9}$ and r=3, we get

$a_n=\dfrac{2}{9}(3)^{n-1}$

Therefore, the correct option is c.