Question

What is the common ratio of the sequence? -2, 6, -18, 54,... −3 −2 3 8

Answer 1

Answer:

-3

Step-by-step explanation:

Consider the geometric sequence:

$b_1=-2\\ \\b_2=6\\ \\b_3=-18\\ \\b_4=54\\ \\....$

Note that

$b_2=b_1\cdot q\\ \\b_3=b_2\cdot q\\ \\b_4=b_3\cdot q\\ \\...$

So,

$6=-2q\\ \\-18=6q\\ \\54=-18q\\ \\...$

From all of these equalities we can state that

$q=-3$

Answer 2

Answer:

r = - 3

Step-by-step explanation:

The sequence is geometric if a common ratio r exists between consecutive terms.

6 ÷ - 2 = - 3

- 18 ÷ 6 = - 3

54 ÷ - 18 = -3

The sequence is geometric with common ratio r = - 3