Question

Find the geometric means in the following sequence.

47,
?
,
?
,
?
,
?, - 789, 929
R
Select one:
a. -6,580, -9,870, -13,160, -16,450
b. 329, 2,303, 16,121, 112,847
C. 2,303, -16,121, 112,847, -789,944
d. -329, 2,303, -16,121, 112,847

Answer 1

d (last choice)

Explanation:

The explicit form of a geometric sequence is
`a_n=a_1 \cdot r^(n-1)` where
`a_1` is the first term while
`r` is the common ratio.

We are given the first term
`a_1=47`.

We are given the sixth term
`a_6=-789929`.

If we divide 6th term by 1st term this is the result:

`(a_1 \cdot r^5)/(a_1 )=(-789929)/(47)`

Simplify both sides:

`r^5=-16807`

Take the fifth root of both sides:

`r=-7`

The common ratio is -7.

So all we have to do is start with the first term and keep multiplying by -7 to get the other terms.

`a_1=47`

`a_2=47(-7)=-329`

`a_3=47(-7)^2=2303`

`a_4=47(-7)^3=-16121`

`a_5=47(-7)^4=112847`

`a_6=47(-7)^5=-789929`

The terms -329,2303,-16121,112847 are what we are looking for in our choices.

That's the last choice.