Question

Find the geometric means in the following sequence.

-9,?,?,?,?,-9,216
Select one:
a. -144, -576, -2,304, -9,231
b. 36, 144, 576, 2,304
c. -720, -1,080, -1,440, -1,800
d. -36, -144, -576, -2,304

Answer 1

Last choice. d.

Explanation:

We are given the first term and the sixth term.

The first term is
`a_1=-9`.

The sixth them is
`a_6=a_1r^5=-9216`.

Let's solve for the common ratio, r.

`-9r^5=-9216`

Divide both sides by -9:

`r^5=1024`

Take the fifth root of both sides:

`r=1024^{(1)/(5)}`

`r=4`

So the common ratio is 4.

`a_1=-9`

`a_2=-9(4)=-36`

`a_3=-9(4)^2=-144`

`a_4=-9(4)^3=-576`

`a_5=-9(4)^4=-2304`

`a_6=-9(4)^5=-9216`