Question

Select the correct answer.
Which explicit function defines this arithmetic sequence?

-351, -343, -335, -327, -319

A.
f(n) = 8n − 359
B.
f(n) = -8n + 359
C.
f(n) = 8n − 351
D.
f(n) = -8n − 351

Answer 1

To find the explicit function that defines the given arithmetic sequence, we first need to determine the common difference:

- The first term is \(-351\).
- The second term is \(-343\).
- The common difference \(d\) is calculated as follows:
\[
d = -343 - (-351) = -343 + 351 = 8
\]

The common difference is \(8\).

The explicit formula for an arithmetic sequence can be defined as:
\[
f(n) = a + (n - 1)d
\]
where:
- \(a\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

Here, \(a = -351\) and \(d = 8\).

Substituting these values into the formula gives:
\[
f(n) = -351 + (n - 1) \cdot 8
\]
Now simplifying this:
\[
f(n) = -351 + 8n - 8
\]
\[
f(n) = 8n - 359
\]

Now, we can compare our derived formula \(f(n) = 8n - 359\) with the options provided. The correct answer is:

**A. \(f(n) = 8n - 359\)**.