Final Answer:
The 84th term of the arithmetic sequence is 1097.
Step-by-step explanation:
1. Finding the common difference:
We can find the common difference of the arithmetic sequence by subtracting the first term from the second term:
31 - 18 = 13
Therefore, the common difference is 13.
2. Finding the 84th term:
To find the 84th term, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1) * d
where:
a_n is the nth term
a_1 is the first term
n is the number of terms
d is the common difference
In this case:
a_1 = 18 (first term)
n = 84 (number of terms)
d = 13 (common difference)
Substituting these values into the formula, we get:
a_84 = 18 + (84 - 1) * 13
a_84 = 18 + 1079
a_84 = 1097
Therefore, the 84th term of the arithmetic sequence is 1097.