Question

1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4
A)15
B)15/2
C)-15
D)1/15
I chose A

2)Find the sum of the infinite geometric series. Sigma sign with infinity symbol above and n=1 below. To the right 20(-1/4)n-1
A)25
B)80/3
C16
D)does not exist
I chose A

3)Find the sum of the infinite geometric series:4+3+9/4+:...
A)16/7
B)16
C)-12
D)does not exist
I chose B

4)Write 0.72 repeating as a fraction.
A)7/9
B)8/11
C)18/25
D)7 and 2/9
I chose B but my book confuses me on how to work it out. I just divided 8 and 11 and I got .72 repeating

5)Find the fifth term of the sequence in which a1=-3,and aN+1=3aN-n
A)-301
B)-99
C)-193
D)-341
I don't know

Answer 1

1. I chose B
2. C
3. Hey, I better start showing you how

1. Plain geometric series
Sn = g(1-r^n)/(1-r)

300 = g (1-3^4) /1-3

300 = g (1-81) / -2

g = 300 (-2/-80)

g = 15/2

2. sigma = g/(1-r)
g=20
r=-1/4
sigma = 20/1.25
= 2000/125
= 400/25
= 16

3. g = 4
r = 3/4
s = 4/(1-3/4)
=16

4. .72 72 72 72 ....
= 72 10^-2 + 72 10^-2 10^-2 +72 (10^-2)^3 ...

this is geometric series with
g = 72*10^-2
r = 10^-2
so

s = 72*10^-2/(1-.01)
= .72/.99
= 8/11

I do not understand the last one.

Answer 2

thanks for the help. are you possitive they are correct?

Answer 3

Oh good heavens, always check anything I do!