Question

Which sentence is NOT a geometric progression?

Answer 1

c) 3, 6, 9 12  is NOT a geometric progression

Further explanation

Geometry sequences are series of numbers that have a constant ratio

or can be interpreted:

Each number is obtained by multiplying the previous number by a constant

The sequence can be:

a, ar, ar², ar³, ... etc.

Can be formulated

$\large {\boxed {\bold x_n = ar ^ {n-1}}}$

where:

a is the first term, and

r is the common ratio

So we have to see the series has the same ratio or not

a. $\dfrac{5}{1}=\dfrac{25}{5}=5\to \rm geometric\:progression$

b. $\dfrac{8}{4}=\dfrac{16}{8}=2\to \rm geometric\:progression$

c.$\dfrac{6}{3}\neq \dfrac{9}{6}\to \rm not\:geometric\:progression$

d. $\dfrac{6}{2}=\dfrac{18}{6}=3\to \rm geometric\:progression$

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Keywords : a geometric sequence, the first term, the common ratio

Answer 2

Answer:

The correct option is c.

Step-by-step explanation:

A geometric progression has common ratio. It means the ratio between any two constitutive terms are same.

(a)

The given sequence is

1, 5, 25, 125

$r_1=\frac{5}{1}=5$

$r_2=\frac{25}{5}=5$

$r_3=\frac{125}{25}=5$

It is a geometric progression because it has a common ratio, i.e., 5.

(b)

The given sequence is

4, 8, 16, 32

$r_1=\frac{8}{4}=2$

$r_2=\frac{16}{8}=2$

$r_3=\frac{32}{16}=2$

It is a geometric progression because it has a common ratio, i.e., 2.

(c)

The given sequence is

3, 6, 9 12

$r_1=\frac{6}{3}=2$

$r_2=\frac{9}{3}=\frac{3}{2}$

$r_3=\frac{12}{9}=\frac{4}{3}$

$r_1\neq r_2\neq r_3$

It is not a geometric progression. Therefore the correct option is c.

(d)

The given sequence is

2, 6, 18, 54

$r_1=\frac{6}{2}=3$

$r_2=\frac{18}{6}=3$

$r_3=\frac{54}{18}=3$

It is a geometric progression because it has a common ratio, i.e., 3.