Question

Find the missing terms in the following geometric sequence.

Answer 1

Answer: D. 36, 108

Step-by-step explanation:

In the geometric series the ratio of two consecutive term is constant and this ratio is called the common ratio,

Let n be the common ratio of the given series,

Then the GP will be,

12, 12×n, 12×n×n, 324,

Again by the definition of Geometric series,

$\frac{12n}{12} = \frac{324}{12n^2} \implies n^3 = 27\implies n = 3$

Thus, the required series is,

12, 12×3, 36×3, 324

= 12, 36, 108, 324

⇒ Option D is correct.

Answer 2

Answer:

The correct option is d. 36, 108

Explanation:

We are given the below series:

12,___, ___, 324

In geometric series every number after the first is found by  multiplying the previous term by a fixed number.

The given series can be written as:

$12 \times 3^{0}=12$

$12 \times 3^{1}=36$

$12 \times 3^{2}=108$

$12 \times 3^{3}=324$

Therefore, the option d. 36, 108 is correct