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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

User Ray Zhang
by
8.0k points

1 Answer

6 votes

Answer:

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.

User Artem Zinoviev
by
8.5k points