How many terms are in the geometric sequence?
\[3, 3 \sqrt 2, 6, \dots, 96, 96 \sqrt 2, 192, \dots, 768, 768 \sqrt{2}\]
+9519 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.
