Answers

  • Brainly User
2016-07-20T11:59:45+08:00
The sequence:

3/2, a₂,  a₃,  a₄.  a₅,  a₆, 96

the five geometric means between 3/2 an 96 are:
a₂,  a₃,  a₄,  a₅,  a₆

Step 1:  Find the common ratio

an = a₁  (r)^{n-1}

an ⇒ a7 = 96      n = 7     a₁ = 3/2

96 = 3/2  (r)^{7-1}

2/3 [96 = 3/2  r^{6} ] 2/3

64 = r⁶

 \sqrt[6]{64}  \sqrt[6]{r}

r = 2   common ratio

Step 2:  Find the 5 geometric means

a₂ = a₁ (2)    
a₂ = 3/2 (2)
a₂ = 3

a₃ = a₂ (2)
a₃ = 3 (2)
a₃ = 6

a₄ = a₃ (2)
a₄ = 6(2)
a₄ = 12

a₅ = a₄ (2)
a₅ = 12 (2)
a₅ = 24

a₆ = a₅ (2)
a₆ = 24 (2)
a₆ = 48

ANSWER:  3, 6, 12, 24, 48

The seguence is:  3/2,  3,  6,  12,  24,  48,  96
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