Question

What kind of sequence is this?

–12, 48, –192, 768, ...

Answer 1

To determine the type of sequence, let's look at the pattern in the terms given:

The sequence is:
- \( a_1 = -12 \)
- \( a_2 = 48 \)
- \( a_3 = -192 \)
- \( a_4 = 768 \)

Now, let's examine the ratio between consecutive terms to see if it's a geometric sequence.

1. **From \( a_1 \) to \( a_2 \)**:
\[
\frac{a_2}{a_1} = \frac{48}{-12} = -4
\]

2. **From \( a_2 \) to \( a_3 \)**:
\[
\frac{a_3}{a_2} = \frac{-192}{48} = -4
\]

3. **From \( a_3 \) to \( a_4 \)**:
\[
\frac{a_4}{a_3} = \frac{768}{-192} = -4
\]

Since the ratio between each pair of consecutive terms is the same, namely \(-4\), this sequence is a **geometric sequence** with a common ratio of \(-4\).

Thus, the sequence can be described as a geometric sequence with a first term of \(-12\) and a common ratio of \(-4\).