Answers

2016-07-20T11:07:53+08:00
  • Brainly User
2016-07-20T11:44:28+08:00
Sequence:

1/2, ____, ____,  4
a₁,    a₂,      a₃   a₄

Step 1:  Find the common ratio, r:

an = a₁ ( r)^{n-1}

a₁ = 1/2        a₄ = 4     n = 4

4 = 1/2  (r)^{4-1}

4 = 1/2 (r³)

2/1 [ 4= 1/2 r³ ] 2/1

8 = r³

 \sqrt[3]{3}= \sqrt[3]{8}

r = 2

Step 2: Find the two geometric means, a₂ and a₃

a₂ = a₁(2)                                 a₃ = a₂ (2)
a₂ = 1/2 (2)                               a₃ = 1(2)
a₂ = 1                                        a₃ = 2

ANSWER:  The two geometric means are 1 and 2

The geometric sequence is:  1/2,  1,  2,  4
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