What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −8? an = 4(−2)n − 1; all integers where n ≥ 0 an = 4(−2)n − 1; all integers where n ≥ 1 an = 4(−12)n − 1; all integers where n ≥ 1 an = 4(−12)n − 1; all integers where n ≥ 0

Option B is right

Step-by-step explanation:

Given:

There is a geometric sequence with first term =4

and second term =-8

We know that a geometric sequence is a sequence of numbers, in which each successive number is got by multiplying the previous number by a fixed value called common ratio.

First term is called a.

and common ratio is denoted by r.

The terms would be

Here we have a=4 and ar =-8

So r =common ratio =-2

nth term we mean n can take values as 1,2.....

So general term

is right answer

Hence option b.

up

step-by-step explanation:

the orientation of the parabolas can easily be found by analysing the power of x and y and their signs. if x is squared , parabola opens up and also if its coefficient is negative it opens down. if y is squared , the parabola opens right and also if its coefficient is negative it opens left. however in order to do the above analysis our equation must be in standard form .

our parabola is

which is not standard form of any parabola . hence we square on both hand side and convert it into standard form.

hence we see that x is squared and its coefficient is non negative . there for it opens up.

- "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."