Question

What is the explicit rule for this geometric sequence?

2/9,2/3,2,6,...




a) an=3(29)^n−1

b) an=3(29)^n

c) an=29⋅3^n−1

d) an=29⋅3n

Answer 1

Option 3 just did the test

Explanation:

Answer 2

Given:

The geometric sequence is
`(2)/(9),(2)/(3),2,6,...`

To find:

The explicit formula for the given geometric sequence.

Solution:

We have, a geometric sequence

`(2)/(9),(2)/(3),2,6,...`

Here,

First term :
`a=(2)/(9)`

Common ratio :
`r=((2)/(3))/((2)/(9))`

`r=(2)/(3)* (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=(2)/(9)` and r=3, we get

`a_n=(2)/(9)(3)^(n-1)`

Therefore, the correct option is c.