Question
find the common ratio: 4, -16, 64, -256, ...
Answers
Answered by
GPT-4o mini
To find the common ratio of the given geometric sequence (4, -16, 64, -256, ...), you can divide any term by the previous term in the sequence.
1. Divide the second term by the first term:
\[
\text{Common Ratio (r)} = \frac{-16}{4} = -4
\]
2. Divide the third term by the second term:
\[
\text{Common Ratio (r)} = \frac{64}{-16} = -4
\]
3. Divide the fourth term by the third term:
\[
\text{Common Ratio (r)} = \frac{-256}{64} = -4
\]
In each case, the common ratio \( r \) is -4.
Therefore, the common ratio of the sequence is \(-4\).
1. Divide the second term by the first term:
\[
\text{Common Ratio (r)} = \frac{-16}{4} = -4
\]
2. Divide the third term by the second term:
\[
\text{Common Ratio (r)} = \frac{64}{-16} = -4
\]
3. Divide the fourth term by the third term:
\[
\text{Common Ratio (r)} = \frac{-256}{64} = -4
\]
In each case, the common ratio \( r \) is -4.
Therefore, the common ratio of the sequence is \(-4\).