Final answer:
The 84th term is calculated as 18 + (83 * 13), which equals 1097. To find the 84th term of the arithmetic sequence 18, 31, 44, ..., we use the formula for the nth term of an arithmetic sequence.
Step-by-step explanation:
The question asks us to find the 84th term of the arithmetic sequence 18, 31, 44, ... . To do this, we can use the formula for the nth term of an arithmetic sequence:
Tn = a + (n - 1) * d
Where:
- Tn is the nth term of the sequence
- a is the first term in the sequence
- n is the term number
- d is the common difference between terms
For this sequence, the first term (a) is 18 and the common difference (d) can be found by subtracting the first term from the second term: 31 - 18 = 13.
Let's plug these values into the formula to find the 84th term:
T84 = 18 + (84 - 1) * 13
Calculating the right side of the equation:
T84 = 18 + (83 * 13)
T84 = 18 + 1079
T84 = 1097
Therefore, the 84th term of the arithmetic sequence is 1097.