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

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 $\dfrac{3}{2}.$

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

$\dfrac{a(2)}{a(1)}=\dfrac{24}{16}=\dfrac{3}{2},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{36}{24}=\dfrac{3}{2},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{54}{36}=\dfrac{3}{2},~~.~~.~~.$

Thus, the required common ratio of the given geometric sequence is $\dfrac{3}{2}.$