Final answer:
The 12th term (s12) in the series is found using the arithmetic sequence formula. With a common difference of -9, the 12th term is calculated as -104.
Step-by-step explanation:
To find the 12th term (s12) in the series -5, -14, -23, -32, ..., we must first determine the pattern of the series. Looking at the given numbers, we see that each term is 9 less than the previous term. This indicates that the series follows an arithmetic sequence with a common difference of -9.
To find the 12th term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1) * d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.
In this case, a_1 = -5 (the first term), d = -9 (the common difference), and n = 12 (since we are looking for the 12th term).
So, s12 = -5 + (12 - 1) * (-9) = -5 - 11 * 9 = -5 - 99 = -104.
The 12th term (s12) of the series is -104.