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If b is positive, what is the value of b in the geometric sequence 16, a, 18, b?

 Aug 5, 2022
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Let the common ratio be \(r\).

 

We have \(16r^2 = 18\), meaning \(r^2 = {18 \over 16}\). Taking the positive root(I'll challenge you to find why), we have \(r = \sqrt {18 \over 16} = {\sqrt{18} \over \sqrt{16}} = {\sqrt 2 \sqrt 9 \over 4} = {3 \sqrt 2 \over 4}\)

 

So, \(b = 18 \times {3 \sqrt 2 \over 4} = \color{brown}\boxed{27\sqrt 2 \over 2}\)

 Aug 6, 2022

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