Final answer:
The 82nd term of the arithmetic sequence -10, 6, 22, ... is found using the formula for the nth term of an arithmetic sequence. With a common difference of 16, the 82nd term is 1286.
Step-by-step explanation:
To find the 82nd term of the arithmetic sequence -10, 6, 22, ..., we need to determine the common difference and the first term of the sequence. The common difference (d) can be found by subtracting the first term from the second term: d = 6 - (-10) = 16. Now, the nth term (a_n) of an arithmetic sequence can be found using the formula a_n = a_1 + (n-1)d, where a_1 is the first term and n is the term number.
Using this formula, the 82nd term (a_82) can be calculated as follows:
a_82 = a_1 + (82-1)d
= -10 + (81)(16)
= -10 + 1296
= 1286
Therefore, the 82nd term of the arithmetic sequence is 1286.