Question

What is the linear function equation for the arithmetic sequence an=−12+(n−1)⋅(−5)
?(1 point)
Responses

y=−5x−12
y equals negative 5 x minus 12

y=−12x−5
y equals negative 12 x minus 5

y=−7x−5
y equals negative 7 x minus 5

y=−5x−7
y equals negative 5 x minus 7

Answer 1

To find the equation of the linear function that represents the given arithmetic sequence \( a_n = -12 + (n - 1) \cdot (-5) \), we first need to rewrite it in a more standard form.

Starting with the given expression:

\[
a_n = -12 + (n - 1)(-5)
\]

We can distribute \(-5\):

\[
a_n = -12 - 5(n - 1)
\]

This simplifies to:

\[
a_n = -12 - 5n + 5
\]

Combining the constant terms:

\[
a_n = -5n - 7
\]

This shows that the arithmetic sequence can be expressed as a linear function:

\[
y = -5x - 7
\]

Thus, the correct choice from your responses is:

**y = -5x - 7**