We are given a geometric sequence: $-1, 2, -4, 8, \dots$, and we need to find the 7th term ($a_7$) using the formula provided:

$a_n = a_1 \cdot r^{(n-1)}$

Step 1: Identify the first term ($a_1$) and the common ratio ($r$)

• First term ($a_1$): $-1$
• To find the common ratio ($r$), divide the second term by the first term: $r = \frac{2}{-1} = -2$

Step 2: Use the formula for the 7th term

We know $a_1 = -1$, $r = -2$, and $n = 7$.

$a_7 = a_1 \cdot r^{(7-1)} = -1 \cdot (-2)^6$

Step 3: Calculate $(-2)^6$

$(-2)^6 = 64$

Step 4: Final Calculation

$a_7 = -1 \cdot 64 = -64$

Thus, the 7th term of the sequence is $\boxed{-64}$.

Would you like any further details or have any questions?

Here are 5 related questions to explore further:

1. How do you determine if a sequence is geometric?
2. What would happen if the common ratio was a fraction instead of an integer?
3. How would you find the sum of the first 7 terms of this sequence?
4. What if the sequence started at a different first term, how would the 7th term change?
5. Can the common ratio be positive and still have alternating signs in the sequence?

Tip: In geometric sequences, if the common ratio is negative, the signs of the terms will alternate between positive and negative.