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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:

Option c (I cannot........Florida) is the appropriate response.

Step-by-step explanation:

The given statement of query seems to be incomplete. Please find the attachment of the complete problem below.

The other three given alternatives aren't related to the question. Thus option c is the correct one.

Answer:

=5b-3

Step-by-step explanation:

(7b -4) + (-2b+1).

Remove parenthesis;

7b-4+-2b+1

Group like terms;

=7b-2b-4+1

Add similar element

7b-2b=5b

=5b-4+1

Add/subtract the numbers

=5b-3

Answered by the ONE & Only #QUEEN herself aka #DRIPPQUEENMO

HOPE THIS HELPED!!!

Answer:

a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]

b)

The balance after 1 year is of $10,768.644

The balance after 2 years is of $11,500.91

The balance after 5 years is of $14,010.25.

The balance after 10 years is of $19,467.15

c)

The doubling time is of 10.54 years.

Step-by-step explanation:

Continuously compounded interest:

The amount of money earning after t years, with interest compounded continuously, is given by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.

a) Find the exponential function that describes the amount in the account after time t, in years.

Suppose that $10,083 is invested at an interest rate of 6.8% per year

This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]

So

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 10083(1+0.068)^t[/tex]

[tex]A(t) = 10083(1.068)^t[/tex]

b) What is the balance after 1 year? 2 years? 5 years? 10 years?

After 1 year:

[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]

The balance after 1 year is of $10,768.644

After 2 years:

[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]

The balance after 2 years is of $11,500.91.

After 5 years:

[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]

The balance after 5 years is of $14,010.25.

After 10 years:

[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]

The balance after 10 years is of $19,467.15.

c) What is the doubling time?

This is t for which [tex]A(t) = 2A(0)[/tex]. So

[tex]A(t) = A(0)(1.068)^t[/tex]

[tex](1.068)^t = 2[/tex]

[tex]\log{(1.068)^t} = \log{2}[/tex]

[tex]t\log{1.068} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]

[tex]t = 10.54[/tex]

The doubling time is of 10.54 years.

Step-by-step explanation:

{(2)³}⁸×{(2)³}-⁵

2²⁴× 2-¹⁵

2²⁴-¹⁵. ( subtract 24 and 15)

2⁹= 512

So...

8×8×8= 512

hence

8³ Answer

Answer:

No

Step-by-step explanation:

To form a proporion, both would need to be a multiple of the same thing, whcih they aren't

Step-by-step explanation:

  [tex]a^{2} + 10a + 24[/tex]

= [tex]a^{2}[/tex] + 6a + 4a + 24

= a(a + 6) + 4(a + 6)

= (a + 6)(a + 4)

Answer:

solution:

[tex] {a}^{2} + 10a + 24[/tex]

a²+6a+4a+24

a(a+6)+4(a+6)

(a+6)(a+4) is your answer

Answer:

An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

Answer:

Yes, w=5 is a solution for this inequality.

Step-by-step explanation:

w+11<22

If w=5, this is:

5+11<22

16<22, which is true. So w=5 works as a solution

Answer:

Mean:

= (4 + 6 + 9 + 11 + 8 + 13 + 12) / 7

= 63 / 7

= 9 (The sum of the numbers divided by the number of numbers)

Median:

= 4, 6, 8, 9, 11, 12, 13

= 9 (The middle number of a list from least to greatest)

Mode:

= NONE (The number that appears the most in a given list)

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.

Answer:

the first answer maybe?

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

22°

Step-by-step explanation:

<1 is a secant-secant angle (it lies outside the circle, created by two lines that cut through the circle). The measure of a secant-secant angle is half the difference of the measures of the intercepted arcs:

<1=(0.5)(98-54)

<1=(0.5)(44)

<1=22°

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

Answer:

6,0

Step-by-step explanation:

Answer:

[tex]9\frac{4}{9}[/tex]

Step-by-step explanation:

Exact from:

[tex]\frac{85}{9}[/tex]

Decimal Form:

9.4

Mixed Number Form:

[tex]9\frac{4}{9}[/tex]

Give me Brainllest

Answer:

X = 3

Step-by-step explanation:

x= 6 x 1/2

Answer:

18 12

6 22

Step-by-step explanation:

if u understand my handwriting lol

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:

15 m E. B. C. D. that's why I will be there

Answer:

The answer is C) car b travels 11 more miles than car a in one hour

Step-by-step explanation:

Car A: 18/20(60)=54 mph

Car B: 13/12(60) = 65 mph

So car b travels 11 more miles than car a in one hour

Answer:

use photomath it'll slove it for you

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

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:

B

Step-by-step explanation:

Cand D: A= bh

A: A = (a+b)/2h

E: A= 6a^2

Answer:

$15.65

Step-by-step explanation:

$20 + $20 = $40

$40 - $24.35 = $15.65