Answer:
Option 2nd is correct
common ratio between successive terms in the sequence is \(\frac{1}{3}\)
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,....
⇒\(a_1 = 27\)
\(a_2 = 9\)
\(a_3 = 3\) ......
Then by definition of common ratio:
\(r = \frac{a_2}{a_1}=\frac{a_3}{a_2}....\)
Substitute the given values we have;
\(r = \frac{9}{27} = \frac{3}{9}....\)
⇒\(r = \frac{1}{3}\)
Therefore, the common ratio between successive terms in the sequence is \(\frac{1}{3}\)
