Question

What is the common ratio of the geometric sequence 16, 24, 36, 54, ...?

please show me how to do this problem

Answer 1

The common ratio for the geometric sequence is :
32

Step-by-step explanation:

16,24,36,54

We calculate the common ratio r:
r is obtained by dividing a term by its preceding term

1) 2416=32

2) 3624=32

The common ratio for the geometric sequence is :
32

Answer 2

Answer: The required common ratio of the given geometric sequence is
`(3)/(2).`

Step-by-step explanation: We are given to find the common ratio of the following geometric sequence :

16, 24, 36, 54, . . .

We know that

the common ratio of a geometric sequence is the ratio of any term to its preceding term.

For the given sequence, we have

a(1) = 16, a(2) = 24, a(3) = 36, a(4) = 54, . . .

So, we get

`(a(2))/(a(1))=(24)/(16)=(3)/(2),\\\\\\(a(3))/(a(2))=(36)/(24)=(3)/(2),\\\\\\(a(4))/(a(3))=(54)/(36)=(3)/(2),~~.~~.~~.`

Thus, the required common ratio of the given geometric sequence is
`(3)/(2).`