Question

what is the common ratio between successive terms in the sequence? 27, 9, 3, 1, 1/3, 1/9, 1,27,.... 3 1/3 3

Answer 1

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 $\frac{1}{3}$

Answer 2

The common ratio is;
$\frac{9}{27} = \frac{3}{9} = \frac{1}{3}$