Respuesta :
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
[tex]r_1=\frac{5}{1}=5[/tex]
[tex]r_2=\frac{25}{5}=5[/tex]
[tex]r_3=\frac{125}{25}=5[/tex]
It is a geometric progression because it has a common ratio, i.e., 5.
(b)
The given sequence is
4, 8, 16, 32
[tex]r_1=\frac{8}{4}=2[/tex]
[tex]r_2=\frac{16}{8}=2[/tex]
[tex]r_3=\frac{32}{16}=2[/tex]
It is a geometric progression because it has a common ratio, i.e., 2.
(c)
The given sequence is
3, 6, 9 12
[tex]r_1=\frac{6}{3}=2[/tex]
[tex]r_2=\frac{9}{3}=\frac{3}{2}[/tex]
[tex]r_3=\frac{12}{9}=\frac{4}{3}[/tex]
[tex]r_1\neq r_2\neq r_3[/tex]
It is not a geometric progression. Therefore the correct option is c.
(d)
The given sequence is
2, 6, 18, 54
[tex]r_1=\frac{6}{2}=3[/tex]
[tex]r_2=\frac{18}{6}=3[/tex]
[tex]r_3=\frac{54}{18}=3[/tex]
It is a geometric progression because it has a common ratio, i.e., 3.
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
[tex] \large {\boxed {\bold x_n = ar ^ {n-1}}} [/tex]
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. [tex]\dfrac{5}{1}=\dfrac{25}{5}=5\to \rm geometric\:progression[/tex]
b. [tex]\dfrac{8}{4}=\dfrac{16}{8}=2\to \rm geometric\:progression[/tex]
c.[tex]\dfrac{6}{3}\neq \dfrac{9}{6}\to \rm not\:geometric\:progression[/tex]
d. [tex]\dfrac{6}{2}=\dfrac{18}{6}=3\to \rm geometric\:progression[/tex]
Learn more
a geometric sequence
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Keywords : a geometric sequence, the first term, the common ratio
