Final answer:
The formula for finding the nth term of an arithmetic sequence is a_n = a_1 + (n-1)d. Using the information given, we can solve for a_1 and d, and then substitute those values into the formula to find the nth term of the sequence. The equation for the nth term of the sequence is -100n + 507.
Step-by-step explanation:
The correct answer is option: The formula to find the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d
where:
an is the nth term of the sequence
a1 is the first term of the sequence
d is the common difference between terms
Using the information provided, we can solve for a1 and d:
a1 = a3 - 2d = 207 - 2d
a1 = a5 - 4d = 407 - 4d
By equating these two expressions, we can solve for d:
207 - 2d = 407 - 4d
2d - 4d = 407 - 207
-2d = 200
d = -200/2 = -100
Substituting the value of d back into one of the earlier equations, we can solve for a1:
a1 = 207 - 2(-100) = 207 + 200 = 407
Now, we can find the nth term using the formula:
an = a1 + (n-1)d
an = 407 + (n-1)(-100) = 407 - 100n + 100 = -100n + 507
Therefore, the nth term of the sequence is -100n + 507.