Question

For each arithmetic sequence, determine the related function. Then determine if the function is proportional or nonproportional. Explain

a) 1,3,5
b) 2,7,12
c) -3,-6,-9

Answer 1

For each arithmetic sequence, the related function can be determined by examining the pattern of the sequence. If the difference between consecutive terms is constant, then the related function is linear and proportional.

Step-by-step explanation:

For each arithmetic sequence, we can determine the related function by examining the pattern of the sequence. If the difference between consecutive terms is constant, then the related function is linear. The general form of a linear function is y = mx + b, where m is the slope (the common difference) and b is the y-intercept.

a) In the sequence 1, 3, 5, the common difference is 2. So, the related function is y = 2x - 1.

b) In the sequence 2, 7, 12, the common difference is 5. So, the related function is y = 5x - 3.

c) In the sequence -3, -6, -9, the common difference is -3. So, the related function is y = -3x + 0.

All three functions are proportional since they have a constant slope (common difference).