Final answer:
The 100th term of an arithmetic sequence where the first term is 12 and the 24th term is 0 is found to be approximately -10.43 when calculated using the formula for the nth term of an arithmetic sequence with a common difference of -12/23.
Step-by-step explanation:
To determine the value of the 100th term (a100) in an arithmetic sequence where it's given that ax = 12 (where x is assumed to be 1 because it's not specified) and a24 = 0, we use the formula for the nth term in an arithmetic sequence: an = a1 + (n - 1)d, where d is the common difference between terms.
First, we find the common difference using the given terms. We know a24 - a1 = (24 - 1)d, or 0 - 12 = 23d. Solving for d, we get d = -12/23.
Now, we can find the 100th term using the nth term formula. a100 = a1 + (100 - 1)d = 12 + 99(-12/23).
Calculating a100, we find that it equals 12 - (99 × 12/23), which simplifies to 12 - 516/23 or 12 - 22.43 approximately. Therefore, the 100th term, a100, is approximately -10.43.