Question

question
find the common ratio of the geometric sequence $-16, -48, -144, ...$

Explanation:

Step1: Recall common ratio formula

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

Step2: Calculate using first two terms

Take the second term $-48$ and divide by the first term $-16$.
$r = \frac{-48}{-16}$

Step3: Simplify the expression

$\frac{-48}{-16} = 3$

Step4: Verify with next pair

Check with the third and second term: $\frac{-144}{-48} = 3$, confirming consistency.

Answer:

3