Question

What is the linear function equation for the arithmetic sequence an=13+(n−1)(−2) (1 point) Responses y=13x−15 y is equal to 13 x minus 15 y=−2x+15 y is equal to negative 2 x plus 15 y=2x−15 y is equal to 2 x minus 15

Answer 1

To find the linear function equation for the arithmetic sequence given by \( a_n = 13 + (n-1)(-2) \), we can simplify this expression.

1. Start with the given equation:
\[
a_n = 13 + (n-1)(-2)
\]

2. Distribute \(-2\):
\[
a_n = 13 - 2(n-1) = 13 - 2n + 2
\]

3. Combine like terms:
\[
a_n = 15 - 2n
\]

This can be rewritten as:
\[
a_n = -2n + 15
\]

Now, to express it in the form \( y = mx + b \), we can identify \( m = -2 \) and \( b = 15 \).

Thus, the linear function equation is:
\[
y = -2x + 15
\]

So, the correct response is:
**y = -2x + 15**.