To write the recursive formula for the sequence $-1, -5, -25, -125$, observe the pattern:

1. The first term ($a_1$) is $-1$.
2. Each term is obtained by multiplying the previous term by $-5$.

Recursive Formula:

$a_1 = -1$ $a_n = a_{n-1} \cdot (-5), \quad \text{for } n \geq 2$

Explanation:

• The sequence starts at $-1$.
• To get the next term, multiply the current term by $-5$.

Let me know if you need further clarification or more examples!

Related Questions:

1. How can you find the explicit formula for this sequence?
2. What would be the 6th term in this sequence?
3. How do you prove that this sequence forms a geometric progression?
4. What is the sum of the first 5 terms of this sequence?
5. How can you use this recursive formula in programming for generating sequences?

Tip:

Always identify whether a sequence is arithmetic, geometric, or neither before forming its formula!