Answer:
To determine the nature of the sequence 7, 14, 28, 56, 112, let's analyze it:
**Arithmetic Sequence**:
An arithmetic sequence is one in which each term after the first is obtained by adding a constant difference to the previous term.
Let's check if the sequence 7, 14, 28, 56, 112 is arithmetic:
- Difference between 14 and 7: \( 14 - 7 = 7 \)
- Difference between 28 and 14: \( 28 - 14 = 14 \)
- Difference between 56 and 28: \( 56 - 28 = 28 \)
- Difference between 112 and 56: \( 112 - 56 = 56 \)
The differences (7, 14, 28, 56) are not consistent, indicating that the sequence is not arithmetic.
**Geometric Sequence**:
A geometric sequence is one in which each term after the first is obtained by multiplying the previous term by a constant ratio.
Let's check if the sequence 7, 14, 28, 56, 112 is geometric:
- Ratio between 14 and 7: \( \frac{14}{7} = 2 \)
- Ratio between 28 and 14: \( \frac{28}{14} = 2 \)
- Ratio between 56 and 28: \( \frac{56}{28} = 2 \)
- Ratio between 112 and 56: \( \frac{112}{56} = 2 \)
The ratios (2, 2, 2, 2) are consistent, indicating that the sequence is geometric with a common ratio of 2.
Therefore, the sequence 7, 14, 28, 56, 112 is **geometric**.
