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# help with geometric sequence

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If b is positive, what is the value of b in the geometric sequence 16, $$a, 12, b$$?

May 10, 2022

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Since b is positive, the common ratio $$\dfrac b{12}$$ is also positive. Then all the numbers in the sequence are positive.

Using geometric mean, $$a = \sqrt{16 \cdot 12} = 8\sqrt3$$.

We can find the common ratio by calculating the second term divided by the first term, so the common ratio is $$\dfrac{8\sqrt 3}{16} = \dfrac{\sqrt 3}2$$.

Therefore, $$\dfrac b{12} = \dfrac{\sqrt 3}2$$. Multiply both sides by 12 to get $$b = 6\sqrt 3$$.

May 10, 2022