Final answer:
The nᵗʰ term of the arithmetic sequence with a first term of 18 and a second term of -282 is represented by the formula 318 - 300n.
Step-by-step explanation:
The student is asking to find the nᵗʰ term of an arithmetic sequence where the first term (a1) is 18 and the second term (a2) is -282. An arithmetic sequence follows the pattern an = a1 + (n-1)d, where d is the common difference between consecutive terms.
First, we need to determine the common difference (d) of the sequence:
- d = a2 - a1
- d = -282 - 18
- d = -300
Now that we have determined the common difference, the formula for the nᵗʰ term becomes:
- an = 18 + (n-1)(-300)
- an = 18 - 300n + 300
- an = 318 - 300n
Hence, the nᵗʰ term in the sequence is 318 - 300n.