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Geometric sequence

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How many terms are in the geometric sequence?
$3, 3 \sqrt 2, 6, \dots, 96, 96 \sqrt 2, 192, \dots, 768, 768 \sqrt{2}$

May 14, 2022

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Common ratio = (second term)/(first term) = $$\dfrac{3\sqrt2}3 = \sqrt2$$

Therefore, if the nth term of the sequence is $$768\sqrt 2$$, then $$3\left(\sqrt 2\right)^{n - 1} = 768\sqrt 2$$

Then $$\left(\sqrt 2\right)^n = 512$$.

You can calculate the value of n, and 768 sqrt(2) will be the nth term, i.e., there are n terms in the sequence, which I will leave it for you to calculate.

May 14, 2022
edited by MaxWong  May 14, 2022