Answer:
The given sequence is: 7, -42, 252, -1512, ...
EXPLANATION
To find the recursive formula for the n-th term, we need to identify the pattern in the sequence.
Looking at the terms, we can observe that each term is obtained by multiplying the previous term by -6.
Let's break it down step by step:
1. The first term (n = 1) is 7.
2. To find the second term (n = 2), we multiply the first term by -6: 7 * (-6) = -42.
3. To find the third term (n = 3), we multiply the second term by -6: -42 * (-6) = 252.
4. To find the fourth term (n = 4), we multiply the third term by -6: 252 * (-6) = -1512.
So, we can say that the n-th term (aₙ) is obtained by multiplying the (n-1)th term (aₙ₋₁) by -6.
Recursive formula: aₙ = aₙ₋₁ * (-6)
To summarize, the recursive formula for the given sequence is aₙ = aₙ₋₁ * (-6), where aₙ represents the n-th term of the sequence.