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The nth terms of sequence 1 ; 5 ; 11 ; 19  is n² + n + -1   and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3  .

The differences (referred to as first differences) between every two successive terms are the same, then it is called an arithmetic sequence (which is also known as a linear sequence). But if the first differences are NOT same, and instead, the second differences are the same, then the sequence is known as a quadratic sequence.

According to the question

The sequence      1   ,   5   , 11  ,   19

First difference :       4      6       8

Second difference:        2     2  

1.1.1>

Now, expression for the nth term of the sequence.

Quadratic equation

ax² + bx + c

at n= 1

a + b + c = 1 -----------------(1)

At n = 2

4a + 2b + c = 5 ------------------(2)

At n = 3

9a + 3b + c = 11 -------------------(3)

solving equation

Subtracting equation (3) from (2)

9a + 3b + c = 11

-4a - 2b - c = -5

5a + b = 6 ----------------------(4)

Subtracting equation (2) from (1)

4a + 2b + c = 5

-a  - b - c = -1  

3a + b = 4 ---------------------------- (5)

Subtracting  equation (5) from  (4)

5a + b = 6

-3a - b = -4

2a = 2

a = 1

Putting value in equation (5)

3a + b = 4

3*1 + b = 4

b = 1

Substituting the value in equation (1)

a + b + c = 1

1 + 1 + c = 1

c = -1

Substituting the value in the quadratic equation

x² + x + -1

For nth term

n² + n + -1  

1.1.2>

Term of the sequence is 2549

Now,

using the nth term

n² + n + -1  = 2549

n (n+1) = 2550

n (n+1) = 50 * 51

n = 50

1.2>  sequence of numbers is given:   -2   ,-3   ,-6   ,-11

                First difference =                       -1     -3    -5

               Second difference =                       -2    -2    

1.2.1 >

Now , expression for the nth term of the sequence.

Quadratic equation

ax² + bx + c

at n= 1  

a + b + c = -2 -----------------(1)

At n = 2

4a + 2b + c = -3 ------------------(2)

At n = 3

9a + 3b + c = -6 -------------------(3)

solving equations  

Subtracting equation (3) and (2)

9a + 3b + c = -6

-4a - 2b - c = 3

5a +b = -3 ----------------(4)

Subtracting equation (2) and (1)

4a + 2b + c = -3

-a - b - c = 2

3a + b = -1 -------------------(5)

Now,

Subtracting equation (5) and (4)

5a +b = -3

-3a - b = 1

2a = -2

a = -1

Putting value of a in equation (5)

3*-1 + b = -1

b = 2

Substituting values in equation (1)

-1 + 2 + c = -2

c = -3

nth term

-n² + 2n -3  

1.2.2>the sequence of numbers will never contain a positive term.  

because its first term is -ve and difference between consecutive term is always -ve. or as per nth term n² is a -ve term .

Hence, the nth terms of sequence 1 ; 5 ; 11 ; 19  is n² + n + -1   and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3  .

To know more about Quadratic equation here:

https://brainly.com/question/2263981

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Answer:

33 units²

Step-by-step explanation:

1/2(11 x 6) = 33 units²

Answer:

$88.00

Step-by-step explanation:

66=3/4x

66/.75=66*4/3=88

Answer:

c the data shows positive associations with trend line

Answer:

no she needs $2.20 more

Step-by-step explanation:

2+ 1.10+.05= $3.15

$5.35 - $3.15 = the answer

Answer:

the cost of the plan in the case when 388MB is used is $101.64

Step-by-step explanation:

The computation of the cost of the plan in the case when 388MB is used

Given that

One time fee is $35

And, it involves 150 MB of data usage

Also for the extra megabyte it charges $0.28

So for 388MB, the cost of the plan is

= $35 + 0.28 × (388 MB - 150 MB)

= $35 + $66.64

= $101.64

Hence, the cost of the plan in the case when 388MB is used is $101.64

Answer:B

Step-by-step explanation:

Answer:

$15.65

Step-by-step explanation:

$20 + $20 = $40

$40 - $24.35 = $15.65

Answer. False... All rectangles are parallelograms.

I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!

Answer: False

Step-by-step explanation:

Parallelogram does not include some of rectangle's property

If you need a more graphical explanation, refer to the attachment below.

Answer:

the first answer maybe?

Step-by-step explanation:

9514 1404 393

Answer:

  6 hours

Step-by-step explanation:

The old machine produces widgets at the rate of ...

  (24 widgets)/(3 h) = 8 widgets/h

The new machine produces widgets at the rate of ...

  (48 widgets)/(4 h) = 12 widgets/h

The total rate of production of the two machines is ...

  (8 +12) widgets/h = 20 widgets/h

Then the time required to produce 120 widgets is ...

  (120 widgets)/(20 widgets/h) = 6 h

Working together, the two machines can produce 120 widgets in 6 hours.

Answer:

6

Step-by-step explanation:

took the test

Answer:

20 quarts.

Step-by-step explanation:

Because there are 20 quarts in 5 gallons.

Answer:

[tex]4x {}^{2} - 36 \\ = (2x + 6)(2x - 6) \\ hence \: option \: b \: is \: correct[/tex]

Answer:

Soooooo, for Part A I got answer choice D.

I didn't want to overthink it like I normally do with everything else in life so i was like, there are 3 boxes on the side and 4 boxes on the bottom, so 3 times 4= 12.

Now i know that the area of the neighborhood is 12 blocks and 20 blocks equals a mile. 12 is obviously not 20, twelve is actually a little bit over half of twenty or .50%, so the best answer would be D.60%.

Now part B, i dont know bout all that, I can only give you half an answer. Copped out at the mention of the word Density XD. Hope that first part helped tho.

Answer:

70 m and 60 m

Step-by-step explanation:

The formula for the area of a rectangle is length ⋅ width.

The area of the pasture of 4200 meters.

70 ⋅ 60 = 4200.

The formula for the perimeter of a rectangle is side + side + side + side.

The perimeter of the rectangle is 260 meters.

70 + 60 + 70 + 60 = 260.

Therefore, the length and width of this pasture are 70 meters and 60 meters.

Answer:

B

Step-by-step explanation:

find slope which is -2 then plug into equation y=mx+b to find constant of 3

Answer:

Step-by-step explanation:

(1,5 ) indicates that for every 1 book they make 5 dollars so the point means that for every book they sell they make 5 dollars.

Step-by-step explanation:

don't see any points to pick from however the following would lie on the graph

(0,12)

(1,8)

(2,4)

(3,0)

(4,-4)

Answer:

x = 24.5

Step-by-step explanation:

the angles form a straight line, and a straight line equals to 180°

=> (5x + 8) + (3x - 24) = 180

=> 8x = 196

=> x = 24.5

His percent error is 25% because 12 is 75% of 16. 100 - 75 = 25

Answer:

75% correct and 25%error

Step-by-step explanation:

As 12÷16×100=75%

The error =100-75=25%

Answer:

C

Step-by-step explanation:

C is the answer becasue range is not classified as a measure of central tendency

Answer:

Keep it up

Step-by-step explanation:

Your teacher is nice for posting it to you iif you can not solve again brick it to me and followed me

Answer:

24 bows can be made with 4 yards of ribbon

Answer:

V = 5412 cm^3

Step-by-step explanation:

[tex]v \: = 41 \times 22 \times 6 \\ \\ v = 5412 \: {cm}^{3} [/tex]

I hope that is useful for you :)