Question

What is the common ratio of the sequence?

-2, 6, -18, 54,...

−3
−2
3
8

Answer 1

r = - 3

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

Answer 2

-3

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`