What is the nth term rule of the quadratic sequence below?
-4,-3,0,5, 12, 21, 32,...
I need help quick!!

Answers

Answer 1

Answer:

The nth term = n^2 - 2n - 3.

Step-by-step explanation:

Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c

Example 1

Write down the nth term of this quadratic number sequence.

-3, 8, 23, 42, 65...

Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.

Sequence = -3, 8, 23, 42, 65

1st difference = 11,15,19,23

2nd difference = 4,4,4,4

Step 2: If you divide the second difference by 2, you will get the value of a.

4 ÷ 2 = 2

So the first term of the nth term is 2n²

Step 3: Next, substitute the number 1 to 5 into 2n².

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Differences = -5,0,5,10,15

Now the nth term of these differences (-5,0,5,10,15) is 5n -10.

So b = 5 and c = -10.

Step 5: Write down your final answer in the form an² + bn + c.

2n² + 5n -10

Example 2

Write down the nth term of this quadratic number sequence.

9, 28, 57, 96, 145...

Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.

Sequence = 9, 28, 57, 96, 145...

1st differences = 19,29,39,49

2nd differences = 10,10,10

Step 2: If you divide the second difference by 2, you will get the value of a.

10 ÷ 2 = 5

So the first term of the nth term is 5n²

Step 3: Next, substitute the number 1 to 5 into 5n².

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Differences = 4,8,12,16,20

Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.

Step 5: Write down your final answer in the form an² + bn + c.

5n² + 4n


Related Questions

A sixth grade class has 12 boys and 24 girls.

For every 2 boys, there are 4 girls. Do you agree with this statement? Explain.

Answers

Answer:

Yes

Step-by-step explanation:

The best way to solve this question is to use ratios. The first ratio to make is 12:24. This represents how there are 12 boys for 24 girls. Ratios remain equivalent as long as both sides of the ratio are simplified by the same number. So, you can divide both sides by 6. When you divide both sides you get 2:4. Therefore, there are 2 boys for 4 girls.

Write each phrase as a numerical or algebraic expression. 189 subtracted from t

Answers

Answer:

t-189

Step-by-step explanation:

if 3/ 4 part of the total number of students in a class are girls how much percent are boys ​

Answers

Answer:

1

Step-by-step explanation: because 3 are girls and 3 + 1 equals 4 its 1

Answer:

1/4 or 25% are boys

Step-by-step explanation:

3/4 + 1/4 = 4/4

75% + 25% = 100%

I don’t know how i’m supposed to do this it’s basically dividing a fraction with a fraction or something

Answers

It is 1.3 in decimal form

Answer:

84/63

Step-by-step explanation:

when you are dividing two fractions that is the equal of multiplying the upper one with the opposite of the one below

There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is
5\12
There are 84 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.

Answers

Answer:

49 red marbles

Step-by-step explanation:

We should first make 5/12 have a base of 84, so that'll be

(5*7)/(12*7)=35/84. So we have 35 blue marbles and all the rest are red, so 84-35=49

DUBS

Please consider giving me a brainliest! Thank you.

the point (-2,6) is on a line with a slope of 3/4. If the point -8,k) is also on the same line what is the value of k

Answers

For a point with a slope 3/4 and which passes through the points  (-2, 6) and (-8, k), the value of k is 1.5

The line passes through the points (-2, 6) and (-8, k)

That is, [tex]x_1=-2, y_1=6, x_2=-8, y_2=k[/tex]

The slope of the line, m = 3/4

The formula for calculating the slope of a line is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute   [tex]x_1=-2, y_1=6, x_2=-8, y_2=k, m = \frac{3}{4}[/tex] into the formula above

[tex]\frac{3}{4} = \frac{k-6}{-8-(-2)} \\\\\frac{3}{4} = \frac{k-6}{-8+2}\\\\\frac{3}{4} = \frac{k-6}{-6}\\\\-6(3)=4(k-6)\\\\-18=4k-24\\\\4k=-18+24\\\\4k=6\\\\k=\frac{6}{4} \\\\k=1.5[/tex]

Therefore, the value of k is 1.5

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According to the glossary, what are large meteors that enter the Earth's atmosphere?

A) Active galaxy
B) Blueshift
С) Coma
D) Bolide​

Answers

B) Blueshift bbbbbbbbbbb

Calculating interest

Answers

Answer:

Simple Interest is calculated using the following formula: SI = P × R × T, where P = Principal, R = Rate of Interest, and T = Time period. Here, the rate is given in percentage (r%) is written as r/100. And the principal is the sum of money that remains constant for every year in the case of simple interest.

Step-by-step explanation:

hope this helps

d
=

(
x
2

x
1
)
2
+
(
y
2

y
1
)
2
Evaluate
d
if
(
x
1
,
y
1
)
=
(

3
,
4
)
and
(
x
2
,
y
2
)
=
(

2
,
4
)
.

Answers

Please comment on this so I can see the full question

I will give brainliest who ever answers fastest what is 1+1=?

Answers

Answer:

2

Step-by-step explanation:

Like and give 5 star rating

Twelve football teams are playing in a league. Each team played each of the other teams exactly once. How many matches were played in the league? *
1 point
a. 72
b. 66
c. 11
d. 132

Answers

Each team will play with 11 other teams. Hence each team plays 11 games. Hence a total of 11*12 =132 games but since each game involves two teams divide 132/2 = 66 so B

Round 18.527 to the nearest tenth.

Answers

Answer:18.53

Step-by-step explanation:

7 rounding up will end up to three

Answer:

18.5

Step-by-step explanation:

Pls helpp
1: Find the slope:

Answers

m = (3 - 1) / (0 - (-4)) = 2 / 4 = 2

Create a probability model for the outcome of performing 2 spins. What is the probability of NOT landing on yellow or red at all?

Answers

Using the concept of probability, the probability of not landing on yellow or red at all is 1/4.

Creating a square model of the two spins :

Red(R) ; Blue(B) ; Green(G) ; Yellow(Y)

___ R ___ B ___ G ___ Y

R_ RR __ RB __ RG __ RY

B_ BR __ BB __ BG __ BY

G_ GR __GB __ GG __GY

Y_ YR __ YB __ YG __ YY

Sample space = = 16

Combinations without red and yellow :

{BB, BG, GB, GG} Number of selections without red or yellow = 4

Recall :

Probability = required outcome / Total possible outcomes

P(without Red or Yellow) = 4/16 = 1/4

Hence, the probability of not landing on yellow or red at all is 1/4.

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The angle of elevation from the tip of the shadow to the top of the tree is 36°. Find the distance from the top of the tree to the tip of the shadow. Round the answer to the nearest tenth. A. 26. 7 feet b. 30. 2 feet c. 40. 8 feet d. 42. 9 feet.

Answers

The expression that represents the required distance is [tex]\mathbf{ s = \frac{h}{0.5878}}[/tex]

The given parameters are:

[tex]\mathbf{\theta =36^o}[/tex] --- the angle of elevation to the top of the tree

To do this, we make use of the following representations

s represents the distance from the tip of the shadow to the top of the treeh represents the height of the tree

The distance (s) is then calculated using the following sine ratio

[tex]\mathbf{ sin(\theta) = \frac{h}{s}}[/tex]

Make s the subject

[tex]\mathbf{ s = \frac{h}{sin(\theta)}}[/tex]

Substitute [tex]\mathbf{\theta =36^o}[/tex]

[tex]\mathbf{ s = \frac{h}{sin(36)}}[/tex]

Evaluate sin(36)

[tex]\mathbf{ s = \frac{h}{0.5878}}[/tex]

The height of the tree is not known.

Hence, the expression that represents the required distance is [tex]\mathbf{ s = \frac{h}{0.5878}}[/tex]

Read more about elevations and distance at:

https://brainly.com/question/14550522

The expression that represents the required distance is

The given parameters are:

--- the angle of elevation to the top of the tree

To do this, we make use of the following representations

s represents the distance from the tip of the shadow to the top of the tree

h represents the height of the tree

The distance (s) is then calculated using the following sine ratio

Make s the subject

Substitute

Evaluate sin(36)

The height of the tree is not known.

Hence, the expression that represents the required distance is

Read more about elevations and distances at:

brainly.com/question/14550522

#SPJ4

The basic Sl unit for measuring mass is the liter. True False​

Answers

Step-by-step explanation:

False

The SI unit of mass is Kilogram ( Kg)

The height of a ball in feet is modeled by f(x) = -16x² +96x, where x is the time in seconds after it is hit. How long is the ball in the air?

Answers

Answer:

The answer is 144 feet and it will be in the air for 6 sec

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

Like and give 5 star rating

What is the equation of this graphed line?



Enter your answer in slope-intercept form in the box.
__________

Answers

Answer:

y = 2x +2

Step-by-step explanation:

The general slope-intercept equation of a line is y=mx+b , where m is the slope and b is the y-intercept ( where the line intersects the y-axis)

From the graph we see that

m= difference in y/difference in x = (6 - -6)/ (2- -4) = 12/6 = 2

m=2 is the slope

b is where the line cuts the y-axis and is at 2

b=2 is the y-intercept

Substitute m and b in the general equation to find the equation of the graphed line.

y = 2x +2

leslie weighs her marbles in a jar and the scale reads 474 grams. The empty jat weighs 439 grams. each marble weighs 5. How many marbles are in the jar

Answers

I’d say 8 marble are in the jar

Somebody please help

Answers

Answer:

c/  y=20x

Step-by-step explanation:

Old McDonald's 3 hens lay the same number of eggs one week. This gives Old McDonald's wife enough eggs for two recipes. One recipe requires 10 eggs and the other recipe requires 2 eggs. How many eggs did each hen lay?

Answers

I think the answer is 4 because you add the 10 and 2 and you get 12 and then divide that by how many hens there are (3). The answer is 4

It takes 39 pounds of seed to completely plant a 4-acre field.
How many acres can be planted per pound of seed?

Answers

Answer:

0.1

Step-by-step explanation:

at the grocery store, abdullah purchased 3 pounds of mac and cheese for $7.50 what does mac and cheese cost per pound?

Answers

Answer:

It costs $0.4 per pound of mac and cheese.

Step-by-step explanation:

3/7.50 = 0.4

Hope this helped. :)

Two lines are
perpendicular if the
of their
А
and
Lline are also perpendicular.

Answers

If a line is perpendicular to one of the

two given parallel lines then it is also perpendicular to the other line.

As we know that by the theorem of perpendicular transversal theorem that in the plane, if a transverse is perpendicular to one or two parallel lines, then it is perpendicular to the third line. ... Since, they do not touch or interact with each other they are said to be parallel to each other.

Thnx for marking me as brainlist

need #5 and #6 please

Answers

Answer:

Step-by-step explanation:

Ritta purchased a package of stickers. She noticed 4 out of every 5 stickers where purple. Which table shows the relationship between the number of purple stickers, p, and the total number of stickers, t?

Answers

Answer:

4:5

Step-by-step explanation:

I don't see the table but since it is 4 out of every 5 stickers are purple, the ratio would be 4:5, 4/5, or 4 to 5. It doesn't really matter, because all of these mean the same thing.

Tell me if I'm wrong :)

Write the equation of the line in fully simplified slope-intercept form.

Answers

Y=-5x-8
It is 5 down and 1 right so it’s -5 and -8 is from the y- intercept where it crosses

help ! which of the following are the roots of the given quadratic equation ?

[tex]2 {x}^{2} + 18x + 36 = 0[/tex]
a. 6

b. -6

c. 3

d. -3..​

Answers

Answer:

The roots are {-6, -3}

Step-by-step explanation:

We are given four possible roots.  To determine whether or not a particular possible root is actually a root, we use synthetic division.  If the remainder is zero, we may conclude that this is actually a root.

Determine whether or not -3 is a root.  Setting up synthetic division, we get

-3  /  2    18     36

              -6    -36

     ---------------------

      2       12     0

Since the remainder is zero, -3 is a root.

Try -6:  Is this a root of 2x + 12?  Setting up synthetic division, we get

-6    /    2     12

                  -12

      ----------------

          2        0

The remainder is again zero, so -6 is also a root of the original equation.

The roots are {-6, -3}

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The Correct choices are ~

b and d

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve ~

[tex]2 {x}^{2} + 18 {x}^{} + 36 = 0[/tex]

[tex]2 {x}^{2} + 12x + 6x + 36 = 0[/tex]

[tex]2x(x + 6) + 6(x + 6) = 0[/tex]

[tex](2x + 6)(x + 6) = 0[/tex]

There's two cases here,

Case # 1 - when 2x + 6 = 0

[tex]2x + 6 = 0[/tex]

[tex]2x = - 6[/tex]

[tex]x = - 6 \div 2[/tex]

[tex]x = - 3[/tex]

Case # 2 - when x + 6 = 0

[tex]x + 6 = 0[/tex]

[tex]x = - 6[/tex]

Hence, the roots are -3 and -6 ~

Please can someone help with rearranging formulae? Will mark brainliest!

Answers

Answer:

look at the picture ..........

help me with this please and thank you​

Answers

Step-by-step explanation:

a.

1) if A(2;9) and B(6;17), then it is possible to make up the equation of the required line according

2) the rule:

[tex]\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A};[/tex]

3) if to substitute the coordinates of A&B into the rule, then:

[tex]\frac{x-2}{6-2}=\frac{y-9}{17-9}; \ => \ \frac{x-2}{4}=\frac{y-9}{8}; \ => \ \frac{x-2}{1}=\frac{y-9}{2};[/tex]

or 2x-y+5=0 or y=2x+5 (slope-interception form).

P.S. note, the suggested solution is not the shortest one. This task can be solved if to make up the system of two equations in slope-interception form.

b. see the attached picture (the required line is red colour);

c. f(4)=13. Short explanation: if to substitute the coordinate x=4 into the equation y=2x+5, then y=2*4+5=13;

d. the domain is (-∞;+∞), the range is (-∞;+∞).

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