Answer:
B and D
Step-by-step explanation:
6 times 3 equals 18
18 times 3 equals 54
54 times 3 equals 162
Answer: The correct options are
(B) 6, 18, 54, 162, 486, . . .
(D) -4,,-2, -1, -0.5, -0.25, -0.125, . . .
Step-by-step explanation: We are given to select all the sequences that are geometric.
We know that a sequence <a(n)> is geometric is there exists a common ratio r such that
[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=~~.~~.~~.[/tex]
Option (A) :
Here, the given sequence is
2, 5, 8, 11, 14, 17, . . .
We see that
[tex]\dfrac{a(2)}{a(1)}=\dfrac{5}{2}\neq \dfrac{a(3)}{a(2)}=\dfrac{8}{5}.[/tex]
So, this sequence is not geometric and the option (A) is not correct.
Option (B) :
Here, the given sequence is
6, 18, 54, 1562, 486, . . .
We see that
[tex]\dfrac{a(2)}{a(1)}=\dfrac{18}{6}=3,\\\\\dfrac{a(3)}{a(2)}=\dfrac{54}{18}=3,\\\\\dfrac{a(4)}{a(3)}=\dfrac{162}{54}=3,~~.~~.~~.~~=3.[/tex]
So,
[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.[/tex]
Therefore, the sequence is a geometric sequence and so the option (B) is CORRECT.
Option (C) :
Here, the given sequence is
2, 3, 5, 8, 13, 21, . . .
We see that
[tex]\dfrac{a(2)}{a(1)}=\dfrac{3}{2}\neq \dfrac{a(3)}{a(2)}=\dfrac{5}{3}.[/tex]
So, this sequence is not geometric and the option (C) is not correct.
Option (D) :
Here, the given sequence is
-4, -2, -1, -0.5, -0.25, -0.125, . . .
We see that
[tex]\dfrac{a(2)}{a(1)}=\dfrac{-2}{-4}=\dfrac{1}{2},\\\\\dfrac{a(3)}{a(2)}=\dfrac{-1}{-2}=\dfrac{1}{2},\\\\\dfrac{a(4)}{a(3)}=\dfrac{-0.5}{-1}=\dfrac{1}{2},~~.~~.~~.[/tex]
So,
[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.~~=\dfrac{1}{2}[/tex]
Therefore, the sequence is a geometric sequence and so the option (B) is CORRECT.
Thus, (B) and (D) are the correct options.
