Question

what is the common ratio between successive terms in the sequence?
2, -4, 8, -16, 32, -64, ...

-2

-6

6

2

Explanation:

Step1: Recall common ratio formula

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

Step2: Calculate using first two terms

Take the second term \(-4\) and the first term \(2\). Then \( r=\frac{-4}{2}=-2 \).

Step3: Verify with other terms

Check with third and second term: \(\frac{8}{-4}=-2\). Check with fourth and third term: \(\frac{-16}{8}=-2\). All give the same ratio.

Answer:

\(-2\) (corresponding to the option: \(-2\))