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For an arithmetic sequence, f(1) = -3, and the common difference is -1. What is the function?

A. f(n) = -3 - n
B. f(n) = -3 + n
C. f(n) = -3n
D. f(n) = -3n - 1

1 Answer

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Final answer:

The function for the arithmetic sequence is f(n) = -3 - n.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In this case, the common difference is -1.

To find the function for this arithmetic sequence, we can use the formula f(n) = a + (n-1)d, where f(n) is the nth term of the sequence, a is the first term, and d is the common difference.

Given that f(1) = -3 and the common difference is -1, we substitute these values into the formula to get f(n) = -3 + (n-1)(-1). Simplifying this expression, we get f(n) = -3 - (n-1) = -3 - n + 1.

Therefore, the function for the arithmetic sequence is f(n) = -3 - n, which corresponds to option A.

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