Final answer:
The 93rd term of the arithmetic sequence with a common difference of 19 is 1742, found using the formula for an arithmetic sequence term.
Step-by-step explanation:
To find the 93rd term of the arithmetic sequence given by -6, 13, 32, we first need to determine the common difference. We do this by subtracting the first term from the second term and the second from the third.
The difference between the second and the first term is: 13 - (-6) = 19
The difference between the third and the second term is: 32 - 13 = 19
Since the common difference is consistent, we have verified that the sequence is indeed arithmetic and the common difference is 19.
The nth term of an arithmetic sequence can be found using the formula: 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.
Applying this formula to find the 93rd term:
a_93 = -6 + (93 - 1)× 19
a_93 = -6 + (92)× 19
a_93 = -6 + 1748
a_93 = 1742
Therefore, the 93rd term of the arithmetic sequence is 1742.