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7 January, 13:09

The second termn in a geometric sequence is 20. The fourth termn in the same sequense is 45/4, or 11.225. What is the common ratio in this sequence?

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Answers (2)
  1. 7 January, 13:33
    0
    t2=ar^ (2-1)

    20=ar

    then

    t4=ar^ (4-2)

    45/4=ar. r

    45/4=20. r

    45/80=r
  2. 7 January, 14:40
    0
    r=±0.75

    Step-by-step explanation:

    Given:

    a2 = 20

    a4 = 45/4

    As a geometric sequence has a common ratio and is given by:

    an=a1 (r) ^n-1

    where

    an=nth term

    a1=first term

    n=number of term

    r=common ratio

    Now

    a2=20=a1 (r) ^ (2-1)

    20=a1 (r) ^1

    20=a1*r

    Also

    a4=45/4=a1 (r) ^ (4-1)

    45/4=a1r^3

    (a1*r) r^2=45/4

    Substituting value of 20=a1*r

    (20) r^2=45/4

    r^2=45/4 (20)

    r^2=0.5625

    r=±0.75!
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