Question

what is the common ratio of the sequence? -2, 6, -18, 54,... 3 -3 -2 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 \( 6 \) and divide by the first term \( - 2 \): \( r=\frac{6}{-2}=-3 \).

Step3: Verify with other terms

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

Answer:

\( -3 \) (corresponding to the option with text "−3")