Final answer:
To determine the 18th term in the arithmetic sequence, we need to find the common difference. By setting up equations using the given expressions and solving for x, we find the value of the first term. With the common difference and first term, we can use the formula to determine the value of the 18th term.
Step-by-step explanation:
To determine the numerical value of the 18th term in an arithmetic sequence, we need to find the common difference between the terms. In an arithmetic sequence, the difference between consecutive terms is constant.
Given that the first three terms are X+2, 3x-8, 4x+2, we can set up the following equations:
- 3x-8 - (X+2) = (4x+2) - (3x-8)
- 2x-10 = x+10
- x = 20
Now that we know the value of x, we can substitute it back into the expression for the first term: X+2 = 20+2 = 22.
The common difference is then 2x-8 = 2(20)-8 = 32. The formula to find the value of the nth term in an arithmetic sequence is: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
Using this formula, we can find the value of the 18th term: a18 = 22 + (18-1)32 = 22 + 544 = 566.