Let's analyze the sequence: 2, 14, 98, 686.

Step 1: Check for a common difference (Arithmetic Sequence)

An arithmetic sequence has a constant difference between consecutive terms.

• $14 - 2 = 12$
• $98 - 14 = 84$
• $686 - 98 = 588$

Since the differences between consecutive terms are not the same, this sequence is not arithmetic.

Step 2: Check for a common ratio (Geometric Sequence)

A geometric sequence has a constant ratio between consecutive terms. To check if the sequence is geometric, divide each term by the previous term:

• $\frac{14}{2} = 7$
• $\frac{98}{14} = 7$
• $\frac{686}{98} = 7$

Since the ratio is constant ($r = 7$), this is a geometric sequence with a common ratio of $r = 7$.

Conclusion:

The sequence $2, 14, 98, 686$ is a geometric sequence with a common ratio of $7$.

Would you like more details or have any questions?

Here are some related questions:

1. What is the general formula for a geometric sequence?
2. How can we find the sum of a finite geometric sequence?
3. Can a sequence be both arithmetic and geometric?
4. What is the difference between an arithmetic and a geometric sequence?
5. How does a geometric sequence differ from a harmonic sequence?

Tip: In a geometric sequence, the ratio between consecutive terms is always the same, and this is called the common ratio.