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

Answer:

d (last choice)

Step-by-step 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:

$\frac{a_1 \cdot r^5}{a_1 }=\frac{-789929}{47}$

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.