The question is asking about the correct description of an infinite geometric sequence. Let's analyze the options:

1. The sequence continues without end, and there is a common ratio between the consecutive terms.

   • This is the correct description of an infinite geometric sequence. An infinite geometric sequence has an unending number of terms, and each term is obtained by multiplying the previous term by a fixed constant (the common ratio).

2. The sequence continues without end, and there is a common difference between the consecutive terms.

   • This describes an arithmetic sequence, not a geometric sequence.

3. The sequence contains a limited number of terms, and there is a common difference between the terms.

   • This describes a finite arithmetic sequence, not an infinite geometric sequence.

4. The sequence contains a limited number of terms, and there is a common ratio difference between the consecutive terms.

   • This describes a finite geometric sequence, which is also incorrect for the "infinite" case.

Final Answer:

Option 1: "The sequence continues without end, and there is a common ratio between the consecutive terms."

Would you like me to explain further or go into more examples of geometric sequences?

Related Questions:

1. What is the formula for the $n$-th term of a geometric sequence?
2. How do you calculate the sum of an infinite geometric series?
3. What conditions must be satisfied for an infinite geometric series to converge?
4. How does an infinite arithmetic sequence differ from an infinite geometric sequence?
5. Can the common ratio in a geometric sequence be negative?

Tip:

When working with geometric sequences, remember that the common ratio ($r$) determines the behavior of the sequence. If $|r| < 1$, the terms decrease in magnitude, while if $|r| > 1$, they grow exponentially.