Respuesta :
The common ratio of this sequence is -3. This is evident because the 6/-2 is -3, and we know it is a sequence so the rule consistently applies.
Answer: The required common ratio of the given geometric sequence is -3.
Step-by-step explanation: We are given to find the common ratio of the following geometric sequence :
-2, 6, -18, 54, . . .
We know that
if a(n) denotes the nth term of a geometric sequence, then the common ratio is given by
[tex]r=\dfrac{a_{n+1}}{a_{n}}.[/tex]
For the given sequence, we see that
[tex]\dfrac{a(2)}{a(1)}=\dfrac{6}{-2}=-3,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{-18}{6}=-3,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{54}{-18}=-3,\\\\\vdots[/tex]
Therefore, the common ratio is given by
r = -3.
Thus, the required common ratio of the given geometric sequence is -3.
