Answer:
Option 2nd is correct
common ratio between successive terms in the sequence is [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Common ratio(r) defined as the ratio of a term to the previous term.
Also, this common ratio term is constant.
Given the sequence:
27, 9, 3, 1, 1/3, 1/9, 1/27,....
⇒[tex]a_1 = 27[/tex]
[tex]a_2 = 9[/tex]
[tex]a_3 = 3[/tex] ......
Then by definition of common ratio:
[tex]r = \frac{a_2}{a_1}=\frac{a_3}{a_2}....[/tex]
Substitute the given values we have;
[tex]r = \frac{9}{27} = \frac{3}{9}....[/tex]
⇒[tex]r = \frac{1}{3}[/tex]
Therefore, the common ratio between successive terms in the sequence is [tex]\frac{1}{3}[/tex]
