Respuesta :
Answer:
[tex]\frac{2}{3}[/tex].
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.
[tex]\text{Common ratio of geometric sequence}=\frac{a_2}{a_1}[/tex]
Let us use two consecutive numbers of our sequence in above formula.
[tex]a_2[/tex] will be 12 and [tex]a_1[/tex] will be 18 for our given sequence.
[tex]\text{Common ratio of geometric sequence}=\frac{12}{18}[/tex]
Dividing our numerator and denominator by 6 we will get,
[tex]\text{Common ratio of geometric sequence}=\frac{2}{3}[/tex]
Let us use numbers 8 and 16/3 in above formula.
[tex]\text{Common ratio of geometric sequence}=\frac{\frac{16}{3}}{8}[/tex]
[tex]\text{Common ratio of geometric sequence}=\frac{16}{3*8}[/tex]
[tex]\text{Common ratio of geometric sequence}=\frac{2}{3}[/tex]
Therefore, we get [tex]\frac{2}{3}[/tex] as common ratio of our given geometric sequence.
