Question

Which one is not a geometric progression? 2,6,18,54 or 4,8,16,32 or 3,6,9,12 or 1,5,25,125?

Answer 1

what is gemetric progression

Answer 2

Answer:

A Geometric Progression consists of terms in a series which are related to each other by some manner. The GP is in the form

$a, ar, ar^2, ar^3, ...$

here,

the common difference between the terms is calculated using the formula,

$d=\frac{ar}{a}=r$

1. Given sequence is 2, 6, 18, 54

Here

d = 6/2 = 3

d = 18/6 = 3

d = 54/18 = 3

The difference is common in all the terms i.e., 3, hence this series is a GP.

2. Given sequence is 4, 8, 16, 32

Here

d = 8/4 = 2

d = 16/8 = 2

d = 32/16 = 2

The difference is common in all the terms i.e., 2, hence this series is a GP.

3. Given sequence is 3, 6, 9, 12

Here

d = 6/3 = 2

d = 9/6 = 3/2

d = 12/9 = 4/3

The difference is different in every term, hence this series is not in GP.

4. Given sequence is 1, 5, 25, 125

Here

d = 5/1 = 5

d = 25/5 = 5

d = 125/25 = 5

The difference is common in all the terms i.e., 5, hence this series is a GP.

Thus, the series 3, 6, 9, 12 is not in GP