Find the nth term of this quadratic sequence

Answers

Answer 1

The nth term of the quadratic sequence is aₙ = n² + 2n

What is a quadratic sequence?

Finding the nth term rule of a quadratic sequence: The nth term rule of a quadratic sequence can always be written in the form an² + bn + c.

To find this rule, we need to find a, b and c

Given data ,

Let the expression be represented as = A

Now , the value of A is

A = 3 , 8 , 15 , 24 , 35 ..

Now , taking the difference of the second term and first term , we get

d₁ = 8 - 3 = 5

d₂ = 15 - 8 = 7

d₃ = 24 - 15 = 9

So , the difference of the numbers in the sequence is odd multiples

Therefore , the sequence goes in the multiples of ( n + 2 )

Now , when n = 1

a₁ = 3

when n = 2

a₂ = 8

So , a₂ = n ( n + 2 )

substituting the value for n = 2 , we get

a₂ = 2 ( 2 + 2 )

a₂ = 2 x 4

a₂ = 8

when n = 3

a₃ = 15

So , a₃ = n ( n + 2 )

substituting the value for n = 3 , we get

a₃ = 3 ( 3 + 2 )

a₃ = 3 x 5

a₃ = 15

Therefore , the nth term of the quadratic sequence will be

aₙ = n ( n + 2 )

aₙ = n² + 2n

Therefore , the sequence is aₙ = n² + 2n

Hence , The nth term of the quadratic sequence is aₙ = n² + 2n

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Related Questions

What is the slope-intercept equation for the linear function represented by the
table?
X
y
O Ay=-¹2-2
OB. y = 2x --2
OC. y =
-2
OD. y = 2x+4
0
-2
2
-1
4
0
6 8
1
2

Answers

The linear equation represented in the table is:

y = (1/2)*x - 2

What is the equation of the line in the table?

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if a line goes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can use the first two points on the table (0, -2) and (2, -1), so we will get:

a = (-1 + 2)/(2 - 0) = 1/2

And because of the point (0, -2) we know that the y-intercept is -2, so we can write:

y = (1/2)*x - 2

The correct option is C.

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Determine the degree measure of one angle of a 45-sided regular polygon.

8,100°
7,740°
172°
180°

Answers

The measure of one interior angle of the 45-sided polygon is (c) 172 degrees

How to determine the measure of one interior angle?

From the question, we have the following parameters that can be used in our computation:

Shape = 45-sided polygon

Parameter to calculate = the measure of one interior angle

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides

In this case

n = 45

Substitute the known values in the above equation, so, we have the following representation

The sum of the interior angles = (45 − 2) × 180∘

Evaluate

The sum of the interior angles = 7740∘

So, the internal angle is

Angle = 7740/45

Evaluate

Angle = 172

Hence, the angle is (c) 172 degrees

Answers

John's average speed for the whole race would be; 12.8 kilometers per hour

How to calculate the average speed?

The first part of the race was 14 km long, and he completed it in 1 hour.

Now, formula for speed is;

Speed = distance/time

Thus, John's speed in the first part of the race would be;

14/1 = 14km/hr

The second part was 18 km long, and he completed this part in an hour and a half. This means that his speed in the second part of the race is;

18/1.5 = 12km/hr

Average speed = Total distance/total time

Total distance for both parts of the race is;

14 + 18 = 32km

Total time for the race is;

1 + 1.5 = 2.5 hours

John's average speed for the whole race would be;

32/2.5 = 12.8 kilometers per hour

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A woman has 8 skirts, 5 blouses, and 5 pairs of shoes. How many different skirt-blouse-shoe outfits can she wear? Any combination

Answers

Answer: A woman has 8 skirts, 5 blouses, and 5 pairs of shoes. This means that she has a total of 8 * 5 * 5 = <<855=200>>200 different skirt-blouse-shoe outfits that she can wear.

Step-by-step explanation: To find the number of different skirt-blouse-shoe outfits that a woman can wear, we need to find the total number of combinations of skirts, blouses, and shoes that she has. To do this, we simply multiply the number of skirts that she has by the number of blouses that she has by the number of pairs of shoes that she has. In this case, the woman has 8 skirts, 5 blouses, and 5 pairs of shoes, so the total number of combinations is 8 * 5 * 5 = 200. This means that she can wear 200 different skirt-blouse-shoe outfits.

How much must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily

Answers

There are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given:

A = Final amount = $25000

P = Initial principle balance

r = interest rate = 5% = 0.05

t = Number of time of years

n = number of times interest applied per time period = 365

Since, the formula for compound interest,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

Plug the values of A, r, n and t in the above formula

[tex]25000 = P(1 + \frac{0.05}{365})^3^6^5^*^4 \\25000 = P(1.0001369863)^1^4^6^0\\25000 = P(1.2213860258)\\P = 20,468.549231702[/tex]

P ≈ 20,468.55

Hence, there are $20468.55 must you deposit now in order to have $25,000 in 4 years in an account getting 5% interest compounded daily.

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Bruno recorded 2/12 of his new album in
August, 1/3 of his new album in July, and the
rest in June.
What fraction of the album did he record in June?

Answers

The fraction of the album he recorded in June is 1/2

How to determine this?

When all the fractions of the album will be = 1

Bruno recorded 2/12 was recorded in August

2/12 to the lowest term = 1/6

And 1/3 was recorded in July

So,

The fraction of the rest of the album in June is unknown

Let fraction recorded in June will be = x

x = 1 - 1/6 - 1/3

x = 1/1 - 1/6 - 1/3

x = [tex]\frac{18 - 3 - 6}{18}[/tex]

x = [tex]\frac{9}{18}[/tex]

x = [tex]\frac{1}{2}[/tex] to lowest term

Therefore, he recorded 1/2 of his Album in June

Answers

The probability of the customer wants to take snack B is 144/320 as they have already taken snack A

and the probability of the customer who has not taken snack A before

wants to take snack A =108/252

What is probability?

It is the ratio of favorable outcome to total possible outcome of an event.

How can we determine the probability in this question?

based on given data, we calculated the number of customers who has taken snack A before may want to take snack B. The customers have not taken snack A yet may want to snack A.

hence, probability to take snack B = 144/320

probability to take A =108/252

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a) The probability a person who has eaten snack A before is 59/143.

b) The probability a person who has eaten snack A before is 84/143

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that the total number of people that are taken for the event is 572.

The number of people who have eaten snack A before is 236.

The number of people who have not eaten snack A before is 336.

Probability = The number of outcomes of favorable event/ Total number of outcomes

The probability getting a person who has eaten snack A before is

= 236/ 572

= 59/143 [Divide denominator and numerator by 4]

The probability getting a person who has not eaten snack A before is

= 336/ 572

= 84/143 [Divide denominator and numerator by 4]

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3. Un barco de exploración de aguas profundas está sacando a un buzo a
razón de 25 pies por
minuto. El buzo está a 200 pies bajo el nivel del mar. ¿Qué tan profundo
estaba el buzo
hace 10 minutos?

Answers

The diver was 450 feet deep in the water 10 minutes ago.

How deep was the diver 10 minutes ago?

Let our D be the depth of the diver 10 minutes ago.

Since diver is pulled out at 25 ft/minute, the depth formula can be written as:

[tex]D - 25t = 200[/tex] where t is the time in minutes.

Substituting t = 10, we have:

[tex]D - 25(10) = 200\\D - 250 = 200\\D = 200 + 250\\D = 450 feet.[/tex]

Translated question "A deep-sea exploration vessel is pulling a diver out to rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?"

Answers

The simplified form in base 3 for ln(3) + ln(9) is 3ln(3)

What is logarithm?

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x = n, in which case one writes x = logb n.

In(9) can be written as ln3^2

which according law of logarithm is 2ln(3)

Expression becomes

ln(3) + 2ln(3) which is 3ln(3)

In conclusion, the simplified form of the expression in base 3 is 3ln(3)

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"x/3" is division

x/3 - 4 = -6

what does x equal?

Answers

Answer:

x = -6

Step-by-step explanation:

-6/3-4= -6

Multiply. Write the answer in simplest form.
4 2/3 x 9/10

Answers

Answer:

[tex] 4\frac{1}{5} [/tex]

Step-by-step explanation:

[tex] 4\frac{2}{3} \times \frac{9}{10} [/tex]

[tex] \frac{14}{3} \times \frac{9}{10} [/tex]

[tex] \frac{126}{30} [/tex]

[tex] \frac{21}{5} [/tex]

Parking Spaces múltipl

Answers

Answer: 7584 Parking Spaces

Explanation:
158 rows x 48 Cars = 7584 parking spaces

Please help asap!!!!!!

Answers

By SAS congruence triangle MLN and triangle OLN are congruent.

What is the congruence theorem?

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, LM≅LO, ∠MLN≅∠OLN.

LM≅LO (Given)

∠MLN≅∠OLN (Given)

LN≅LN (Reflexive property of congruence)

ΔMLN≅ΔOLN (SAS congruence)

∠M≅∠O (CPTC)

MN≅ON (CPTC)

Therefore, by SAS congruence triangle MLN and triangle OLN are congruent.

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Ann is 11 more than two times older than Stacy. If Ann is 59 years old,
solve an equation to determine Stacy's age

Answers

The age of Stacy is 24 years old provided the age of Ann is 59 years old.

What is an equation?

Two or more expressions with an equal sign are defined as an equation.

Given that, Ann is 11 more than two times older than Stacy.

Let the age of Stacy and Ann be s and a respectively, then:

a = 11 + 2s

Substitute a = 59 into the above equation:

59 = 11 + 2s

2s = 59 -11

s = 24

Hence, the age of Stacy is 24 years old provided the age of Ann is 59 years old.

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$2, 900 is invested in an account earning 6.1% interest (APR), compounded quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Answers

Answer: The value of the account after t years can be found using the formula:

Value = 2900 * (1 + 0.0061/4)^(4t)

The annual growth rate, or APR, is 6.1%. When this rate is compounded quarterly, the effective annual growth rate, or APY, is 6.17%, which is the nearest hundredth of a percent.

Therefore, the function showing the value of the account after t years is:

Value = 2900 * (1 + 0.0061/4)^(4t)

And the annual growth rate, or APY, is 6.17%.

Use four of the eight image tiles below to graph the solution to this inequality on the number line. Be sure to cover the entire number line.

Answers

To represent an inequality on a number line, such as x>3, first draw a circle around the number. Fill in the circle if the sign also says equal to (or ).

How do you graph an inequality's solution on a number line?To represent an inequality on a number line, such as x>3, first draw a circle around the number.Fill in the circle if the sign also says equal to (or ).Leave the circle blank if the sign doesn't include equal to (> or ).Equation notation, set notation, interval notation, and solution graph are the four ways to display an inequality.Always begin by separating the variable y from the inequality's left side.Step 2: Replace the inequality symbol with the equality symbol.Step 3: In the X, Y, XY, XY plane, graph the boundary line from step 2.The final step is to shade a portion or one side of the boundary line.

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10+((6-4)*4) equal what

Answers

Answer:

Step-by-step explanation:

6-4=2

2x4=8

10+8=18

Question #8
Cameron read that his favorite NBA team won their game last night by a score of 142 to 124.
Which is true about the digit 2 in each number?

Answers

The true statement is that 2 in 142 represents a greater value than 2 in 124 because 142 > 124.

How to identify the place value of a digit in a number?

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol. The place values on the left ofthe decimal point start as ones, tens, hundreds, and so on.

The place value on the right of the decimal point starts from a point and goes to right as tenths, hundredths, and so on.

We are given that encore or points for an NBA Team are usually as whole numbers.

For example, 1, 2, 3, 4, e.t.c. points of an NBA Team are not in decimals or fractions.

The withiner of points awarded for an NBA match is called Discrete because that can be counted with a given amount of time.

Hence, 2 in 142 represents a greater value than 2 in 124 because 142 > 124.

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Kevin and Randy Muise have a jar containing 83 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $12.95. How many of each type of coin do they have?

Answers

The amounts of each type of coin that they have is given as follows:

Quarters: 44.Nickels: 39.

How to obtain the amounts?

The amounts of each type of coin are obtained using a system of equations, in which the variables are given as follows:

Variable x: amount of quarters.Variable y: amount of nickels.

Kevin and Randy Muise have a jar containing 83 coins, hence:

x + y = 83.

The value of a nickel is of $0.05, while the value of a quarter is of $0.25. The total value of the coins in the jar is $12.95, hence:

0.25x + 0.05y = 12.95.

From the first equation, we have that:

y = 83 - x.

Replacing on the second equation, the amount of quarters is given as follows:

0.25x + 0.05(83 - x) = 12.95

0.2x = 8.8

x = 8.8/0.2

x = 44.

Then the amount of nickels is given as follows:

y = 83 - x = 83 - 44 = 39.

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Stock in a certain company sold for $2.50 per share in June. The price of the stock increased $4.75 after one month. It then decreased $1.25 and $2.45 over the next two months. What was the price of the stock after these changes?
Responses

Answers

Answer: $3.55

Step-by-step explanation:

Started at 2.50 increased 4.75 which means the stock is 7.25 then decreased 1.25 making it 6 then another decrease of 2.45 making it $3.55

What is the slope of the line shown below?

Answers

Answer: -3/2

yeah use rise over run

Answer:

-2/3

Step-by-step explanation:

slope = rise/run

First find the y-intercept (point of crossing on the y-axis (the vertical one)), then find the next point that intercepts a box PERFECTLY, this next point is (4, -2)

Looking at the y-intercept's coordinates (0,1), count how many blocks down it takes to get to to 4 (2 blocks which is the RISE) and now count how many blocks to the right it takes to get to -2 (3 blocks)

Therefore it is 2/3 but it is also negative because it is going DOWN from left to right which is a negative decine

bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental. how many games must be played for the cost to be the same at both places? Define variables and solve the system of equations

Answers

The number of games that must be played for the cost to be the same at both places is 4.

How to solve system of equations?

Bowl o rama charges 2.50 a game plus 2 for shoe rental, and bowling pinz charges 2 a game plus 4 for shoe rental.

The number of games that must be played for the cost to be the same at both places is as follows:

Using system of equation,

let

x = number of games

Hence,

2.50x + 2 = 2x + 4

2.50x - 2x = 4 - 2

0.5x = 2

divide both sides by 0.5

x = 2 / 0.5

x = 4

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The probability of rain on Monday is .1. The probability of rain on Tuesday is .8. What is the probability of rain on both Monday and Tuesday?

Answers

Answer:

The probability of rain on both Monday and Tuesday is .08, or approximately 8%.

Step-by-step explanation:

The probability of an event occurring on two separate days (such as rain on Monday and Tuesday) is calculated by multiplying the probabilities of the two events occurring separately. In this case, the probability of rain on both Monday and Tuesday is given by:

Probability of rain on Monday * Probability of rain on Tuesday = .1 * .8 = .08

Therefore, the probability of rain on both Monday and Tuesday is .08, or approximately 8%.

It's important to note that this probability assumes that the likelihood of rain on each day is independent of the other day. In other words, the probability of rain on Tuesday does not depend on whether or not it rained on Monday. If this is not the case, the probability of rain on both days may be different.

Find tanθ + sinθ for the angle θ shown in the right triangle?

Answers

12.6

Step-by-step explanation:

We need to find the hypotenuse

hyp² = opp² + adj²

hyp²= 2² + 3²

hyp²= 4 + 9

hyp²= 13

hyp=√13

hyp=3.6

sinθ=opp/hyp

sinθ=2/3.6

sinθ=5.6

cosθ=adj/hyp

cosθ=3/3.6

cosθ= 0.8

tan θ=sinθ/cosθ

tanθ= 5.6/0.8

tanθ=7

tan θ+sinθ

=7+5.6

=12.6

Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0

Answers

The correct answer is option is a) x^4 – 6x^2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x^4 = -x^2 + 5.

How do you write a quadratic form?

A quadratic equation can be expressed using the formula au^2+bu+c=0. where u is a mathematical expression. In each case, the leading term's exponent is equal to the middle term's exponent multiplied by two.

What is quadratic standard form?

Standard form refers to the quadratic function f(x) = a(x - h)2 + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.

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(8x + 6) - (x + 4).

Answers

8x+6-x-4

Collect like term

Solution

7x+2

The radius of a circle is 8 meters. What is the circle's area?
r=8 m
Use 3.14 for .

Answers

Answer:

200.96

Step-by-step explanation:

3.14*r²

so 3.14*8²=200.96

Help Which number line shows the solution set to this inequality?
-20 + 9

Answers

Answer:

Step-by-step explanation:

-2x + 9 < x - 9

-2x - x < -9 - 9

-3x < -18

x > -18/-3

x > 6

A tree is currently 8 feet tall and grows 3 feet per year
a. Model this scenario with an arithmetic sequence in explicit form
b. Rewrite the explicit form of the sequence using function notation
c. How tall will the tree be in 12 years?

Answers

Answer:

You have to multiple to get you answer

Step-by-step explanation:

p+ 1.4 ≤ 0.5; p = 0.1

Answers

The inequality expression p + 1.4 ≤ 0.5 is false for p = 0.1

How to determine if the expression is true

From the question, we have the following parameters that can be used in our computation:

p + 1.4 ≤ 0.5;

p = 0.1

Substitute p = 0.1 in p+ 1.4 ≤ 0.5;

So, we have the following representation

0.1 + 1.4 ≤ 0.5;

Evaluate the like terms

This gives

1.5 ≤ 0.5;

The above inequality is false

This is because 1.5 is greater than 0.5

Hence, p + 1.4 ≤ 0.5; p = 0.1 is false