Final answer:
The 66th term of the arithmetic sequence -10, 7, 24, ... is 1095, calculated using the formula for the nth term of an arithmetic sequence.
Step-by-step explanation:
To find the 66th term of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence, which is a_n = a_1 + (n - 1)d, where a_n is the n-th term, a_1 is the first term, and d is the common difference between the terms. First, let's find the common difference by subtracting the first term from the second term: d = 7 - (-10) = 17.
Now that we have the common difference, we can find the 66th term using the formula:
a_66 = a_1 + (66 - 1) × 17
a_66 = -10 + (65 × 17)
a_66 = -10 + 1105
a_66 = 1095
Therefore, the 66th term of the arithmetic sequence is 1095.