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

Question

?(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