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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

  • math - ,

    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.

  • math - ,

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

  • math - ,

    Oh good heavens, always check anything I do!

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