Answer:
Option (b) is correct.
The three terms of the GP are [tex]12,12\sqrt{2},24[/tex] with common ratio [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Consider the given geometric sequence [tex]3\sqrt{2},6,6\sqrt{2}......[/tex]
Geometric sequence is a sequence of numbers where each term is find by multiplying the previous one by a fixed number called the common ratio (r).
[tex]a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots[/tex]
Consider the first two terms of the given GP.
[tex]a=3\sqrt{2},ar=6[/tex] thus r can be find by dividing ar by a,
thus the common ratio is [tex]r=\frac{6}{3\sqrt{2}}=\sqrt{2}[/tex]
Now we have to find the next three terms of GP . so multiply r in given last term to obtain next three terms , we get ,
[tex]6\sqrt{2} \times \sqrt{2}=6\times 2= 12 \\\\\\12 \times \sqrt{2}= 12\sqrt{2}\\\\\\\12\sqrt{2} \times\sqrt{2}=24[/tex]
Thus, the three terms of the GP are [tex]12,12\sqrt{2},24[/tex] with common ratio [tex]\sqrt{2}[/tex].
Option (b) is correct.
