Determine whether the sequence is geometric. If so, find the common ratio. 2, –6, 18, –54,...
a. −1/3
b. 3
c. not geometric
d. 2
e. –3
Check the ratio between terms. If it constant, choose it. For example,
-6/2 = ?
To determine whether a sequence is geometric, we need to check if each term is obtained by multiplying the previous term by a constant value, called the common ratio.
Let's examine the given sequence: 2, -6, 18, -54,...
To find the common ratio, we'll divide each term by its previous term.
-6 ÷ 2 = -3
18 ÷ (-6) = -3
-54 ÷ 18 = -3
As we can see, each term is obtained by multiplying the previous term by -3. Therefore, the given sequence is geometric with a common ratio of -3.
So, the answer is option e. -3.