Question

Determine the common ratio and find the next three terms of the geometric sequence

Answer 1

Answer:

BBBBBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:

Answer 2

Answer:

Option (b) is correct.

The three terms of the GP are $12,12\sqrt{2},24$ with common ratio $\sqrt{2}$

Step-by-step explanation:

Consider the given geometric sequence $3\sqrt{2},6,6\sqrt{2}......$

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).

$a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots$

Consider the first two terms of the given GP.

$a=3\sqrt{2},ar=6$ thus r can be find by dividing ar by a,

thus the common ratio is $r=\frac{6}{3\sqrt{2}}=\sqrt{2}$

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 ,

$6\sqrt{2} \times \sqrt{2}=6\times 2= 12 \\\\\\12 \times \sqrt{2}= 12\sqrt{2}\\\\\\\12\sqrt{2} \times\sqrt{2}=24$

Thus, the three terms of the GP are $12,12\sqrt{2},24$ with common ratio $\sqrt{2}$.

Option (b) is correct.