Final answer:
The 82nd term of the arithmetic sequence -8, 9, 26, ... is 1369. This was calculated using the formula for the nth term of an arithmetic sequence, considering the common difference of 17.
Step-by-step explanation:
To find the 82nd term of the arithmetic sequence — -8, 9, 26, ..., we need to identify the common difference and then apply the formula for the nth term of an arithmetic series. The common difference (d) can be found by subtracting the first term from the second term:
d = 9 - (-8) = 17
Now, using the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
we can find the 82nd term:
a_82 = -8 + (82 - 1)×17
a_82 = -8 + 81×17
a_82 = -8 + 1377
a_82 = 1369
Therefore, the 82nd term of the given arithmetic sequence is 1369.