Is this sequence arithmetic,
geometric
or neither?
3.5. -4, -7.5...

Neither

Step-by-step explanation:

If the sequence was geometric, each term would be multiplied by the same multiplier to get to the next one. We can check if the multiplier is the same by taking a term and dividing it by the term before it. For example,

-4/3.5=-1.14285714

-7.5/-4=1.87500

The multiplier between the terms aren't the same so it's not geometric.

For arithmetic, the distances between each term would be the same, and we can take the same idea from the geometric sequence, but use subtraction instead of division

-4-3,5=-7.5

-7.5-(-4)=-3.5

Again, the distances aren't the same, so it's not arithmetic.

- "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."