Final answer:
The question asks for the nᵗʰ term of an arithmetic sequence with the third term being 998 and the fifth term being 1998. To answer, find the common difference and the first term, and then apply the arithmetic sequence formula to get the nᵗʰ term.
Step-by-step explanation:
The student is asking to find the nth term of an arithmetic sequence, given that the third term is 998 and the fifth term is 1998. To start, we need to find the common difference (d) of the sequence. We know the terms are:
- a3 = a1 + 2d = 998
- a5 = a1 + 4d = 1998
Subtracting the first equation from the second gives:
1998 - 998 = (a1 + 4d) - (a1 + 2d)
Which simplifies to 2d = 1000, so d = 500. Now we simply substitute d back into the first equation to find a1 and then use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, to find the nth term.