Question

What is the common ratio of the sequence. -2,6,-18,54

Answer 1

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 2

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

`r=(a_(n+1))/(a_(n)).`

For the given sequence, we see that

`(a(2))/(a(1))=(6)/(-2)=-3,\\\\\\(a(3))/(a(2))=(-18)/(6)=-3,\\\\\\(a(4))/(a(3))=(54)/(-18)=-3,\\\\\vdots`

Therefore, the common ratio is given by

r = -3.

Thus, the required common ratio of the given geometric sequence is -3.