Question

is this arithmetic or geometric
5.8.12.8,20.48

Answer 1

To determine whether the sequence \( 5, 8, 12, 8, 20, 48 \) is arithmetic or geometric, we need to check the differences (for arithmetic) or the ratios (for geometric) between consecutive terms.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant.

Let's find the differences:
- \( 8 - 5 = 3 \)
- \( 12 - 8 = 4 \)
- \( 8 - 12 = -4 \)
- \( 20 - 8 = 12 \)
- \( 48 - 20 = 28 \)

The differences are \( 3, 4, -4, 12, 28 \), which are not constant. Therefore, it is not an arithmetic sequence.

2. **Geometric Sequence**: In a geometric sequence, the ratio of consecutive terms is constant.

Let's find the ratios:
- \( \frac{8}{5} = 1.6 \)
- \( \frac{12}{8} = 1.5 \)
- \( \frac{8}{12} \approx 0.67 \)
- \( \frac{20}{8} = 2.5 \)
- \( \frac{48}{20} = 2.4 \)

The ratios are \( 1.6, 1.5, 0.67, 2.5, 2.4 \), which are not constant. Therefore, it is not a geometric sequence.

**Conclusion**: The sequence \( 5, 8, 12, 8, 20, 48 \) is neither an arithmetic nor a geometric sequence.