Question

Q1 -
Find the geometric means in the following sequence.

-9, ___, ___, ____, ____, -69,984
A. -324, -1,944, -11,644, -69,999
B. -54, -324, -1,944, -11,664
C. 54, 324, 1,944, 11664
D. -1,080, -1,620, -2,160, -2,700

Q2-
Find Sn for the given geometric series. Round to the nearest hundreth
a1= 0.1 , a5= 814.5, r=9.5
Use the formula: Sn= Sn = a(1 - rn) / (1 - r)
A. 85.5
B. 910.32
C. 736.94
D. 51,380.23

Q3-
Find a1 for the given geometric series. Round to nearest hundredth.
Sn= 47,615 , r= 3, n=5
Use the formula : Sn=a1-a1r^n/1-r
A. 393.51
B. 1,535.97
C. 780.6
D. 9,517

Answer 1

-9, ___, ___, ____, ____, -69,984
so a = -9 and
ar^5 = -69984
r^5 = -69984/-9 = 7776
r = 6
so the 2nd term would be -54, ruling out .....

#2
formula should be: S(n) = a(1 - r^n) / (1 - r) or
= a(r^n - 1) / (r - 1) if |r| > 1 which is our case

why was a5= 814.5 given, we could have found that
so S(n) = -.1(9.5^n - 1)/(9.5-1)
= (-1/85)(9.5^n - 1)

You didn't say how many terms you are adding.
I have a feeling you want S(5) and I see that answer

#3
Sn= 47,615 , r= 3, n=5
a(r^n - 1)/(r-1) = S(n)
a(3^5 - 1)/2 = 47615
a(242) = 95230
a = ... I see my answer