Using the image attached:
We see that the second differences (blue ones) are all equal so we conclude that this is a quadratic sequence.
The quadratic sequence has the form:
$T_{n} = an^{2} +bn +c$

To find the value of a we just divide second difference ( -4 ) by 2:

$a = \frac{-4}{2}= -2$

Now we have:

$T_{n}= -2n^{2} +bn+c$

Substitute $n_{1}$ and $n_{2}$ into the equation above:

$T_{1} = -2(1)^{2} +b(1) +c$

$T_{2} = -2(2)^{2} +b(2)+c$

Since $T_{1}$ = -2 and $T_{2}$ = -8 , after simplification we have:

$b +c =0$
$2b+c=0$

The solution of this system is:

b=0, c =0

The general term is :

$T_{n} = -2n^{2}$

6 0

1 year ago

The chart below describes the speed of four runners. Which runner is the fastest?

tensa zangetsu [6.8K]

Answer:

Runner B

Step-by-step explanation:

speed = distance ÷ time

Runner A: 1 ÷ 8 = 0.125m/ms

Runner B: 2 ÷ 10 = 0.2m/ms

Runner C: 3 ÷ 20 = 0.15m/ms

Runner D: 5 ÷ 30 = 0.17m/ms

Runner B has the highest speed so he is the fastest runner.

6 0

1 year ago

HELP Find the y-intercept of the line on the graph.

DedPeter [7]

The y- intercept is -3
The the slope is -5.

Hope this helps

3 0

2 years ago

Read 2 more answers

Gerry thinks that the points (4,2) and (−1,4) form a line perpendicular to a line with slope 4. Do you agree? Why

faust18 [17]

Answer:

The answer to your question is these lines are not perpendicular.

Step-by-step explanation:

Data

A (4, 2)

B (-1, 4)

slope = m = 4

Perpendicular lines mean that these lines cross and form an angle of 90°. Also, the slope of perpendicular lines is negative reciprocals.

Process

1.- Find the slope of the second line and compare it to the slope given.

slope = $\frac{y2 - y1}{x2 - x1}$

Substitution

slope = $\frac{4 - 2}{-1 - 4}$

Simplification and result

slope = $\frac{-2}{5}$

-2/5 is not a negative reciprocal of 4, so these lines are not perpendicular.

4 0

3 years ago