Question

What is the common ratio for the geometric sequence?

18, 12, 8, 16/3,…

Answer 1

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

Answer 2

2/3

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 = (a_(n) )/(a_(n-1) )`

for n = 2

`r = (a_(2) )/(a_(1) )`

⇒
`r = (12 )/(18 )`

⇒
`r = (2 )/(3 )`

for n = 3

`r = (a_(3) )/(a_(2) )`

⇒
`r = (8 )/(12 )`

⇒
`r = (4 )/(6 )`

⇒
`r = (2)/(3 )`

Thus the common ratio 'r' = 2/3