Question

What is the common ratio for the geometric sequence? 18,12,8,163,… Enter your answer in the box.

Answer 1

Answer:

$\frac{2}{3}$.

Step-by-step explanation:  

We have been given a geometric sequence 18,12,8,16/3,.. We are asked to find the common ratio of given geometric sequence.

We can find common ratio of geometric sequence by dividing any number by its previous number in the sequence.

$\text{Common ratio of geometric sequence}=\frac{a_2}{a_1}$

Let us use two consecutive numbers of our sequence in above formula.

$a_2$ will be 12 and $a_1$ will be 18 for our given sequence.

$\text{Common ratio of geometric sequence}=\frac{12}{18}$

Dividing our numerator and denominator by 6 we will get,

$\text{Common ratio of geometric sequence}=\frac{2}{3}$

Let us use numbers 8 and 16/3 in above formula.

$\text{Common ratio of geometric sequence}=\frac{\frac{16}{3}}{8}$

$\text{Common ratio of geometric sequence}=\frac{16}{3*8}$

$\text{Common ratio of geometric sequence}=\frac{2}{3}$

Therefore, we get $\frac{2}{3}$ as common ratio of our given geometric sequence.