Question

arithmetic or geometric
-3,-18,-108,-648,-3888,....

Answer 1

To determine whether the sequence \(-3, -18, -108, -648, -3888, \ldots\) is arithmetic or geometric, we need to analyze the pattern of the numbers.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant. We can find the differences:
- \(-18 - (-3) = -15\)
- \(-108 - (-18) = -90\)
- \(-648 - (-108) = -540\)
- \(-3888 - (-648) = -3240\)

The differences are \(-15\), \(-90\), \(-540\), and \(-3240\), which are not constant. Hence, this is not an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, each term is multiplied by a constant to get the next term. We can find the ratios of consecutive terms:
- \(\frac{-18}{-3} = 6\)
- \(\frac{-108}{-18} = 6\)
- \(\frac{-648}{-108} = 6\)
- \(\frac{-3888}{-648} = 6\)

Since each term is obtained by multiplying the previous term by \(6\), the sequence is a geometric sequence.

Thus, the sequence \(-3, -18, -108, -648, -3888, \ldots\) is **geometric** with a common ratio of \(6\).