Question

What is the common ratio for the geometric sequence? 18, 12, 8, 16/3,…

Answer 1

Answer:

2/3

Step-by-step explanation:

Given : A geometric sequence : 18, 12, 8, 16/3,…

Solution :

Each term is found by multiplying the previous term by a constant in a Geometric Sequence .

In a Geometric Sequence  common ratio is denoted by r

$r = \frac{a_{n} }{a_{n-1} }$

for n = 2

$r = \frac{a_{2} }{a_{1} }$

⇒$r = \frac{12 }{18 }$

⇒$r = \frac{2 }{3 }$

for n = 3

$r = \frac{a_{3} }{a_{2} }$

⇒$r = \frac{8 }{12 }$

⇒$r = \frac{4 }{6 }$

⇒$r = \frac{2}{3 }$

Thus the common ratio 'r' = 2/3

Answer 2

Basically, what should we multiply each term by to get next term

18 times what=12
what=12/18=2/3

12 times what=8
what=8/12=2/3

common ratio is 2/3