math Question

the 5th term in a geometric sequence is 160. The 7th term is 40. What are the possible values of the 6th term of the sequence

+70
70
+80
80

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  2. 👎 0
  3. 👁 1,140
asked by kristi
  1. 40/160 = r^2, so r=±1/2

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    posted by Steve
  2. a 5 = 160

    a 6 = a 5 * q = 160 * q

    a 7 = a 6 * q = a 5 * q * q = 160 * q ^ 2 = 40

    160 q ^ 2 = 40 Divide both sides by 40

    4 q ^ 2 = 1 Divide both sides by 4

    q ^ 2 = 1 / 4 Take square root of both sides

    q = + OR - 1 / 2

    All number in progression is positive so q = 1 / 2


    a 6 = a 5 * q = 160 * q

    a 6 = 160 * 1 / 2 = 80

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    posted by Bosnian

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