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.