Question:Fibonacci
1. Here are the first 5 terms of a quadratic sequence.
1
3
7
13
21
Find an expression, in terms of n for the nth term of this quadratic sequence.

Answers

Answer 1

9514 1404 393

Answer:

  n² -n +1

Step-by-step explanation:

First differences of the terms of the sequence are ...

  3-1 = 2

  7-3 = 4

  13-7 = 6

  21-13 = 8

Second differences are ...

  4-2 = 2

  6-4 = 2

  8-6 = 2

In a quadratic sequence the coefficient of the squared term is half of the second difference value. Here, that means the squared term will be (2/2)n² = n².

__

We can find the other terms of the quadratic expression by considering the differences between n² and the actual sequence.

The sequence of n² terms is ...

  1, 4, 9, 16, 25

When we subtract these from the actual sequence, we get ...

  1-1 = 0

  3-4 = -1

  7-9 = -2

  13-16 = -3

  21-25 = -4

That is, the amount subtracted from n² is one less than the term number.

The expression for the n-th term is ...

  an = n² -n +1


Related Questions

The length of a rectangular swimming pool is twice its width minus 3 meters. If x represents the width of the swimming pool in meters, which expression represents the length of the swimming pool in meters? A. 2x – 3 B. 2 + x – 3 C. D. 3x – 2

Answers

The answer is A. 2x - 3

Answer:

The answer is A

Step-by-step explanation:

plsdyhdjdjdjdkxkxkxkzkkzkzkzososo​

Answers

The gradient of graph is 2

) In a class of 100 boys and 80 girls, 60% of boys and 60% of girls are members of the Honors Society. In a standardized test 75 boys and 65 girls in the class passed the test. Among those who passed the test 80% are members of the Honors Society. What percent of the nonmembers of the Honors Society passed the test (round it to the closest integer)?

Answers

Step-by-step explanation:

tfffgggggggfffffffffffrrrerrrrrrtttt

30 students : 2 teachers
please help this is due today

Answers

Answer:

It’s a ratio

Step-by-step explanation:

Is that the whole question?

If the function f(x) = 4x+2 and g(x) = 5/2x-4 then which of the following is a false statement?


1) f(0) > g(0)

2) f(-4) = g(-4)

3) f(6) = g(12)

4) g(2) > f(2)

Answers

Answer:2

Step-by-step explanation:

The condition of the function g(2) > f(2) is incorrect. Then the false statement is D.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

If the function f(x) = 4x + 2 and g(x) = (5/2)x - 4.

The value of the function at x = 0, will be

f(0) = 4 × (0) + 2 = 2

g(0) = (5/2) × (0) - 4 = -4

The condition f(0) > g(0) is correct.

The value of the function at x = -4, will be

f(-4) = 4 × (-4) + 2 = -14

g(-4) = (5/2) × (-4) - 4 = -14

The condition f(-4) = g(-4) is correct.

The value of the function f(x) at x = 6 and the value of the function g(x) at x = 12, will be , will be

f(6) = 4 × (6) + 2 = 26

g(12) = (5/2) × (12) - 4 = 26

The condition f(6) = g(12) is correct.

The value of the function at x = 2, will be

f(2) = 4 × (2) + 2 = 10

g(2) = (5/2) × (2) - 4 = 1

The condition g(2) > f(2) is incorrect.

Then the false statement is D.

More about the function link is given below.

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find the area
15 yd
5 yd
21 yd

Answers

Answer:

1,575 yd

Step-by-step explanation:

if wrong sorry

what is 80379567489574938074847*387348973863778 i don't know

Answers

9514 1404 393

Answer:

  31134942986701142516840643442546191966

Step-by-step explanation:

The product is 31134942986701142516840643442546191966.

__

The 38-digit product would normally have to be done in segments on a regular calculator. A computer would have to store this as a quadruple-precision number (128 bits).

Which expression is equivalent to y^3-2y^2+y

Answers

It might be C but I’m not sure about it.

Which could you use to prove triangle AED is congruent to triangle CEB?

Answers

Answer:

Option (C)

Step-by-step explanation:

Given:

In right triangles ΔAED and CEB,

m∠AED = m∠CEB = 90°

DE ≅ BE

AD ≅ BC

To prove:

ΔAED ≅ ΔCEB

                    Statements                         Reasons

1). m∠AED = m∠BC = 90°              1). Given

2). DE = BE                                     2). Given

3). AD = BC                                    3). Given

4). ΔAED ≅ ΔCEB                          4). By HL theorem of congruence

Option (C) is the answer.

Write the equation of the line that is perpendicular to y=-4x+12 (-8,3)

Answers

hey...

y = 4x + 12

3 = 4x8 + 12

3= -32+12

3=-20

3= -20/3

it is the ans. hope it helps you

Find the value of X, I need help solving this.

Answers

Answer:

26

Step-by-step explanation:

add both expressions to equal 90 (bc of the right angle)- x+11+2x+1=90

when you solve, you get x=26

Answer:

A) 26

Step-by-step explanation:

This is a right angle and the measure of a right angle is 90°

x+11+2x+1 = 90° add like terms

3x + 12 = 90° subtract 12 from both sides

3x = 78 divide by 3

x = 26

PLZZZZZZZZZFind each percent increase. Round to the nearest percent. From 42 acres to 72 acres _______

Answers

Answer:

58.333333 percent

Step-by-step explanation:

58 percent

I obviously took 42 divided by 72 times 100

need answer asp please

Answers

answer is y=2x-8 i’m pretty sure

Please help hurry I’ll mark brainliest!!!! It’s due hella soon

Answers

Answer:

17) 6 inches.

18) 4.22 miles repeating

Step-by-step explanation:

17) Since we know that the steel structure is 19.8 feet tall in real life, we can use the scale to find the size on the map. First we can convert 3.3 feet to inches. 3 feet to inches is 36 inches and .3 feet is 3.6 inches. This means that we can write the scale as 1 inch : 39.6 inches. Now, we can convert the 19.8 feet to inches. The answer is 237.6 inches. Next, we can divide 237.6 in. by 39.6 in. which is 6 inches. Now, we can multiply 1 inch by 6 inches to get 6 inches.

18) We can use the same method to solve this question. Note: the numbers will get big. 11.4 miles to inches is 722304 inches. We can now divide this number by 2.7 inches. This will give us 267520 inches. This is also 4.22 miles repeating.

I am not 100% sure about question 18 but I am sure about 17!!!

Hope this Helps!!! :)

WHO WANTS BRANLIEST?!?!?!?!?!?!?!?

Answers

Answer:

I Do

Step-by-step explanation:

WILL RATE THE BRAINLIST Explain how you can prove your observations in question 3 using a traditional proof. You don't need to develop the steps of the proof; simply describe an approach that you might use. Which theorems might appear in your proof? (Hint: Use the two diagonals of the parallelogram to assist you in describing an approach.)

Answers

The two diagonals divide the parallelogram into four triangles. If I can prove that the two triangles opposite one another are congregant. then the corresponding sides of those two triangles must be congregant. These corresponding sides will help show that the lengths of the line segments on either side of the point of intersection are equal, proving bisection. To prove triangle congruency, I can use the properties of the angles formed when parallel lines are cut by a transversal and that opposite sides of the parallelogram are congregant.

Answer:

Rectangles are parallelograms. By definition, opposite sides are congruent and all four angles have the same measure. Drawing the two diagonals of a rectangle divides the rectangle into triangles. If I choose a pair of triangles that each have a different diagonal for a side, I can prove them to be congruent. If the triangles are congruent, the corresponding sides (diagonals of the rectangle in this case) are also congruent.

Step-by-step explanation:

Answer on plato

If the measure of <1 = 112 what is the measure of <6?
112
100
68
180

Answers

Answer:it’s 68

Step-by-step explanation:

I think

Answer:

m∠6=68°

Step-by-step explanation:

∠1 and ∠2 are supplementary angles, which means they add up to 180°

180-112=68

∠2 and ∠6 are corresponding angles, so they are the same

m∠6=68°

Which pair of angles must be supplementary? HURRYYYYY!

Answers

Answer:

1 and 3,  if im wrong i am sorry I have not don this in a long time

Step-by-step explanation:

Answer:

I can't read the numbers correctly but a supplementary angles are angle that equal 180*

Hope this helped a little :)

Step-by-step explanation:

Find the time it takes for $9,200 to double when invested at an annual interest rate of 10%, compoun
continuously.
years
Find the time it takes for $920,000 to double when invested at an annual interest rate of 10%, compounded
continuously.
years

Answers

Answer:

years = natural log (total / principal) / rate

years = natural log (18,400 / 9,200) / 10

years = natural log (2) / 10

years = 0.69314718056 / 10

years = 6.9314718056

and this would be the time for ANY amount of money to double.

Step-by-step explanation:

Josie's Bagel Shop recently sold 3 poppy seed bagels and 3 other bagels. What is the experimental probability that the next bagel sold will be a poppy seed bagel? Simplify your answer and write it as a fraction or whole number, P(poppy seed bagel) Submit​

Answers

Answer:

ffbhjdhjdfahdsfsdfakfawlefgwaheghfgawlygfailwegfalawegfuwlgweilfygweiyaglifwafawegwegerg

Step-by-step explanation:

Hi I need help with this question.
2y+4y=16

Answers

Answer: Your answer is y = 8/3.

Answer:

2.6 repeated

Step-by-step explanation:

6y = 16

16/6 = 6y/6

2.6 repeating

Write an equivalent expression to 3^2/3 • 8√ 3^4

Answers

Answer:

I do not know

Step-by-step explanation:

⚠️NEED HELP ASAP ⚠️The following polygons are similar. Solve for x.

Answers

G it’s 6 answer hope it helps sorry if I wrong

Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for play. Each pair of wings is made with 3/4 yard of fabric. The fabric cost $8 dollars per yard. Yo apply properties of multiplication in the following steps to find the total cost of the fabric. 3. Use the associative and commutative properties to rearrange the terms in the expression to make it easier to calculate. Explain why the rearranged expression is easier to work with write your answer in the space below

Answers

Answer:

It would cost $6 per butterfly wing, which multiplied by 13, gives 78.

Step-by-step explanation:

Treat 1 yard of fabric like the fraction 4/4, if this 1 fabric is equal to $8, then 3/4 of the fabric will be $6. That is for one pair of butterfly wings, there's 13 of those so multiply $6 by 13. It's easier this way because we know how much 1 fabric costs, but we don't know what 3/4 of it does, so we treat 1 yard of fabric as the fraction 4/4. This way we can simplify in a relatively easier way.

Answer:

he will need 9.75 yards of fabric i got that from 3/4 x 13= 9.75.

it will cost 78 dollars to buy all the fabric to make the wings. 6x13=78

instead of using 3/4 per butterfly wing we round it to 4/4 that way instead of having to find the price of 3/4 you get the answer and just take 2 dollars for every wing

Step-by-step explanation:

(2, 3) and (6, 8) m=

Answers

Answer: M = 5/4

Step-by-step explanation:

Answer:

I think m=5/4

Step-by-step explanation:

Which is the equation of the line, in general form, with a point (-5,0) and an undefined slope? a. y+5=0
b. x+5=0​

Answers

Y+5=0
If we subtract 5 both sides we get y=-5

Stacey is making pancakes. She has 2 quarts of milk. The recipe calls for 12 fluid ounces of milk. How many ounces of milk will she have after making the pancakes?​

Answers

Answer:

heir ht eit theeir t erehr ther eht ere there there hterh there jt there htererh there ht ereh the the the the the the thetthe they they they they they   tyh ththbey they theyetheir theitr te there ther there the there htere h

Step-by-step explanation:

4x5=20/// 20-12=8// 8+2=10 and there you go 10 is your answer

The amount of milk left after making the pancakes is 52 fluid ounces.

What is a Ratio?

A ratio indicates the number of times one number contains another.

Given that, Stacy has 2 quarts of milk.

Since there are 32 fluid ounces in one quart, it follows:

1 quart = 32 fluid ounces

2 quart = 64 fluid ounces

Therefore, Stacy has 64 fluid ounces of milk.

Now, she used 12 fluid ounces of milk in making pancakes, therefore, the amount of milk left after making the pancakes is:
64 - 12

= 52

Hence, the amount of milk left after making the pancakes is 52 fluid ounces.

To learn more about ratios, click here:

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State the x-intercept of the function 6x−2y=18

Answers

Answer:

Step-by-step explanation:

6x

Find the factors.
36
Find the factors.
48
Find the quotient.
0.5334 divided by 0.06
Find the quotient.
75.10 divided by 10

Answers

Answer:

Step-by-step explanation:

36

=

 

48

=

0.5334

=

0.06

=

75.1

=

10

=

First three common multiples of 4 5 and 10

Answers

20 40 60 these are the first three
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