Find the formula for the nth term of the sequence: 0,7,18,33,52

t(n) = 2n² + n - 3

Step-by-step explanation:

Given sequence:

Find the formula for nth term t(n)

Sequence is neither arithmetic nor geometric, analyzing:

First level difference

Second level difference

As there are two levels, the formula should be in the form of:

Trying the formula with the known terms:

Going back to previous equations to find remaining coefficients:

So the formula becomes:

t(n) = 2n² + n - 3

c

c

c

c

c

c

c

cc

c

step-by-step explanation:

- "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."