Question

which function describes the arithmetic sequence shown? -5, -7, -9, -11, -13, ... a ( f(x) = -3x + 2 ) b ( f(x) = -2x + 3 ) c ( f(x) = -3x - 2 ) d ( f(x) = -2x - 3 )

Explanation:

Step1: Recall arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(f(x)=a_1+(x - 1)d\), where \(a_1\) is the first term and \(d\) is the common difference. Here, \(a_1=-5\) and \(d=-7-(-5)=-2\).

Step2: Substitute values into formula

Substitute \(a_1=-5\) and \(d = - 2\) into the formula:

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We can also check by plugging in \(x = 1\): \(f(1)=-2(1)-3=-5\) (matches the first term), \(x = 2\): \(f(2)=-2(2)-3=-7\) (matches the second term), etc.

Answer:

D. \(f(x)=-2x - 3\)