Question

which function describes the arithmetic sequence shown? -1, 1, 3, 5, 7, 9, 11, 13, ... a $f(x) = 2x - 3$ b $f(x) = 3x - 2$ c $f(x) = 2x + 3$ d $f(x) = 3x + 2$

Explanation:

Step1: Recall arithmetic sequence formula

The general formula for an arithmetic sequence is \( f(x)=a+(x - 1)d \), where \( a \) is the first term and \( d \) is the common difference. Here, \( a=-1 \), \( d = 1-(-1)=2 \). So \( f(x)=-1+(x - 1)\times2=-1 + 2x-2=2x-3 \).

Step2: Verify with options (optional)

• For option A: When \( x = 1 \), \( f(1)=2\times1-3=-1 \); \( x = 2 \), \( f(2)=2\times2-3 = 1 \), which matches the sequence.
• For option B: \( x = 1 \), \( f(1)=3\times1-2 = 1

eq-1 \), eliminate.

• For option C: \( x = 1 \), \( f(1)=2\times1+3 = 5

eq-1 \), eliminate.

• For option D: \( x = 1 \), \( f(1)=3\times1+2 = 5

eq-1 \), eliminate.

Answer:

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