consective term of a sequence have values 2, -1,1/2,-1/4,and 1/8 of the following, which describe the sequence

The given sequence is: 2, -1, 1/2, -1/4, 1/8.

This is a **geometric sequence** because each term is obtained by multiplying the previous term by a constant factor (common ratio). 

To find the common ratio (\(r\)):
- From \(2\) to \(-1\): \(-1 / 2 = -1/2\)
- From \(-1\) to \(1/2\): \(1/2 / -1 = -1/2\)
- From \(1/2\) to \(-1/4\): \(-1/4 / 1/2 = -1/2\)
- From \(-1/4\) to \(1/8\): \(1/8 / -1/4 = -1/2\)

The common ratio is \(r = -1/2\).

Thus, the sequence can be described as a **geometric sequence** with the first term \(a = 2\) and the common ratio \(r = -1/2\).

### General form of the sequence:
The general term of a geometric sequence is given by:
\[
a_n = a \cdot r^{n-1}
\]
Substituting \(a = 2\) and \(r = -1/2\), the general term becomes:
\[
a_n = 2 \cdot \left(-\frac{1}{2}\right)^{n-1}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you derive the formula for the general term of a geometric sequence?
2. Can a geometric sequence have a positive common ratio?
3. How would you calculate the 6th term of this sequence?
4. What happens if the common ratio is 1 or -1 in a geometric sequence?
5. How do you sum the first \(n\) terms of a geometric sequence?

**Tip:** In a geometric sequence, if the common ratio's absolute value is less than 1, the terms will decrease in magnitude over time.

consecutive terms of a sequence have values 2, -1, 1/2, -1/4, and 1/8. Which describe the sequence?

Explore how to identify a geometric sequence with the consecutive terms 2, -1, 1/2, -1/4, and 1/8. Learn the formula for the general term of a geometric sequence and how to find the common ratio. Suitable for students in Grades 9-12.

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