Question

Consider the arithmetic sequence 15, 14 1/3, 13 2/3, 13.

(a) What is the rate of change for the arithmetic sequence?
A) -1/3
B) -1
C) 1
D) 1/3

(b) If the sequence were plotted on a coordinate plane, would the points lie on a line? How do you know?
A) Yes, they would lie on a line because it's an arithmetic sequence.
B) No, they would not lie on a line because it's not an arithmetic sequence.
C) Yes, they would lie on a curve.
D) No, they would not lie on a curve.

(c) What would be the slope of the line on which the points lie?
A) -1/3
B) -1
C) 1
D) 1/3

Answer 1

The rate of change for the arithmetic sequence is -2/3 (considering potential typo in options), which means the points would lie on a straight line if plotted on a coordinate plane. The slope of this line would also be -2/3.

Step-by-step explanation:

When we consider the arithmetic sequence 15, 14 1/3, 13 2/3, 13, we can determine the rate of change by looking at the difference between consecutive terms. The difference between 15 and 14 1/3 is -2/3, and between 14 1/3 and 13 2/3 is -2/3, continuing with -2/3 from 13 2/3 to 13. Therefore, the common difference (rate of change) here is -2/3, which is not listed in the options provided, indicating a potential typo in the options.

For part (b), if the sequence were plotted on a coordinate plane, the points would indeed lie on a line, since an arithmetic sequence has a constant rate of change. This is analogous to a linear equation, where the slope stays constant and any set of points that satisfy the equation will form a straight line.

For part (c), if the arithmetic sequence was plotted on a coordinate plane as per the common difference determined (-2/3), the slope of the line would equate to the rate of change of the sequence, which is the same as the common difference -2/3.