Question

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

Explanation:

Step1: Recall common ratio formula

The common ratio \( r \) of a geometric sequence is found by dividing any term by its previous term, i.e., \( r=\frac{a_{n}}{a_{n - 1}} \).

Step2: Calculate using first two terms

Take the second term \( a_{2} = 6 \) and the first term \( a_{1}=-2 \). Then \( r=\frac{6}{-2}=-3 \).

Step3: Verify with other terms

Check with third and second term: \( \frac{-18}{6}=-3 \), and fourth and third term: \( \frac{54}{-18}=-3 \). Consistent.

Answer:

-3