Which of the following is true regarding the sequence below?
7/12, 1/6, -1/4, 2/3
a. the sequence is arithmetic because there is a common difference of -5/12
b. the sequence is arithmetic because there is a common difference of 1.
c. the sequence is not arithmetic because there is no common difference between the values of n.
d. the sequence is not arithmetic because there is no common difference between the values of a_n.

Option D.

Step-by-step explanation:

The given sequence is

Now this sequence will be an arithmetic sequence if there is a common difference.

To check the common difference we will subtract each term from the successive term.

Therefore

So the answer is option D.The sequence is not an arithmetic sequence because there is no common difference between

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."