Question

Find the missing terms in the following geometric sequence.

a.
48, 162
c.
96, 192
b.
116, 220
d.
36, 108


Please select the best answer from the choices provided


A
B
C
D

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,

`(12n)/(12) = (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

The correct option is d. 36, 108

Step-by-step 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 * 3^(0)=12`

`12 * 3^(1)=36`

`12 * 3^(2)=108`

`12 * 3^(3)=324`

Therefore, the option d. 36, 108 is correct