Question

What is the linear function equation for the arithmetic sequence an=13+(n−1)(−2)
(1 point)
Responses

y=2x−15
y is equal to 2 x minus 15

y=−2x+15
y is equal to negative 2 x plus 15

y=13x−15

Answer 1

To convert the arithmetic sequence given by the formula \( a_n = 13 + (n-1)(-2) \) into a linear function equation, we can simplify the expression:

1. Start with the original sequence formula:
\[
a_n = 13 + (n-1)(-2)
\]
2. Distribute \((-2)\) across \((n-1)\):
\[
a_n = 13 - 2(n-1) = 13 - 2n + 2
\]
3. Combine like terms:
\[
a_n = 15 - 2n
\]

To express this in the form \(y = mx + b\), where \(y\) corresponds to \(a_n\) and \(x\) corresponds to \(n\), we can rewrite it as:
\[
y = -2n + 15
\]

This means the correct equation for the linear function is:
\[
y = -2x + 15
\]

Therefore, the correct response is:
**y = −2x + 15** (y is equal to negative 2 x plus 15).