Final answer:
The nth term of the arithmetic sequence is 200n - 185.To find the nth term of an arithmetic sequence, the common difference is determined using known terms and used to calculate the first term. With both the common difference and the first term, the general formula for the sequence can be established.
Step-by-step explanation:
To find the nth term of an arithmetic sequence, we can use the formula:
an = a1 + (n-1)d
where an represents the nth term, a1 is the first term, and d is the common difference.
In this given situation, we know that the third term is 415 and the fifth term is 815.
Let's solve for a1 and d using these two pieces of information:
415 = a1 + 2d
815 = a1 + 4d
By subtracting the first equation from the second equation, we get:
400 = 2d
d = 200
Substituting the value of d into the first equation, we can solve for a1:
415 = a1 + 2(200)
a1 = 415 - 400
a1 = 15
Now that we have the values of a1 and d, we can find the nth term of the sequence. Let's denote it as an:
an = 15 + (n-1)(200)
Thus, the nth term of the sequence is 15 + 200n - 200, which simplifies to 200n - 185.