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# geometric sequence

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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