A recursive rule for a sequence is given. Find the first four terms of the sequence.
f(1) = 2
f(n) = 4. f(n – 1), where n is an integer and n > 2.

Answers

Answer 1

Answer:  

So...

   a0 = -2

   a1 = (a0)2 - 4  =  4 - 4  =  0

   a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...=  02 - 4  = -4  

       For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again

   a3 = (-4)2 - 4 = 12

 

The first four terms in the sequence are -2, 0, -4, 12.

Step-by-step explanation:

This recursive sequence is defined as follows:

 a0 = -2      [the first term]

 an+1 = an2 - 4     [for all other terms, n≥0; note that you cannot find a0 using this line]

 

Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term.  Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0.  This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).

 

To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.

 

That's why (joke) that the dictionary definition of "recursive" is "see recursive."


Related Questions


Jeremy is making a healthy ice cream using only ripe bananas and peanut butter, the recipe makes 4 servings and calls for a ratio of 5
bananas to 3 tablespoons of peanut butter if Jeremy has 30 bananas, how many tablespoons of peanut butter does he need
Tablespoons

Answers

Answer:

can u show me a pic of the question so it is easier

The healthy ice cream Jeremy is making has 30 bananas and requires 18 tablespoons of peanut butter.

What is a ratio?

The ratio describes the amount of quantity in simplest form, a:b can be written as 'a/b' for convenience.

Given the healthy ice cream, Jeremy is making requires 5 bananas and 3 tablespoons of peanut butter.

From the given question itself, we can conclude that bananas and peanut butter are in direct proportion as the increase in one quantity will result in an increase of another quantity and we can write this in proportion and let the no. of tablespoons of peanut butter requires for 30 banans is x.

∴ 5 : 3 : : 30 : x.

Or

5/3 = 30/x.

5x = 90.

x = 18.

So, Jeremy needs 18 tablespoons of peanut butter for the 30 bananas he has.

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A wise man once said, “400 reduced by 3 times my age is 163.” What is his age? ( I need the step by step equation to solve this)

Answers

Answer: the wise man is 79

Step-by-step explanation:

400 - 3x = 163

400–163 =3x

237 = 3x or 3x = 237 or x = 79…

what is the slope for (1,3) and (1,-2)

Answers

Answer:

-6

Step-by-step explanation:

-2-3/1-1

Kevin Fast pulled a CC- 177 Globemaster airplane 8.8m. he plane weighed 188 tons. How many pounds did the lane weigh?

Answers

Answer:

376000 pounds

Step-by-step explanation:

What's required of this question is to convert the given weight of plane from tons to pounds

Given

[tex]Weight = 188\ tons[/tex]

Required

Get pounds equivalent

From standard unit of measurements

[tex]1\ ton = 2000\ pounds[/tex]

Multiply both sides by 188

[tex]188 * 1\ ton = 188 * 2000\ pounds[/tex]

[tex]188\ tons = 376000\ pounds[/tex]

Hence, the weight of the plane in pounds is 376000

Would like to help me with my math homework?
Math homework is on College for Readiness
High School

Answers

Answer:

I could try to help

Step-by-step explanation:

A number with no variable attached is called a what

Answers

Answer:

constants

Step-by-step explanation:

That is, they're the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value.

The term or number with no variable attached is called a constant as in the polynomial or expression.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

A number consists of the expression with no variable.

As we know, the expression is a combination of numbers, variables, and operators.

If we take an example of the polynomial.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm p(x) = a_0+a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

Here a₀ is a constant because the term a₀ has no variables.

Thus, the term or number with no variable attached is called a constant as in the polynomial or expression and the constant value does not change.

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Medicare Hospital Insurance The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. Suppose the benefits are normally distributed with a standard deviation of $460. Round the final answers to at least four decimal places and intermediate z-value calculations to two decimal places.

Answers

Answer:

The answer is "0.0764"

Step-by-step explanation:

Please find the complete question in the attached file.

[tex]\to \mu = \$ \ 4064\\\\\to \sigma = \$ \ 460 \\\\\to \sigma \bar{x} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

        [tex]= \frac{460}{\sqrt{21}}\\\\ = \frac{460}{4.58257569}\\\\=100.3802[/tex]

[tex]\to P(\bar{x}< \$ \ 3920) = \frac{P((\bar{x} - \mu \bar{x})}{\frac{\sigma \bar{x}<(3920 - 4064)}{100.3802)}}[/tex]

[tex]\to P(z < -1.43) = 0.0764 \\\\\to P(\bar{x}< \$ \ 3920) = 0.0764\\\\[/tex]

During a thunderstorm, 4
inches of rain fell in 2 1/2
hours. What was the rate of rainfall in inches per hour?

Answers

Answer: 1.6 in per hour

Answer:

hourly rate.

Step-by-step explanation:

As others have noted, it is a simple mathematical division problem (4/2.5) and the average is 1.6 inches per hour.

However, if this is for sizing civil works such as culverts or plumbing storm water drainage systems to mitigate flooding, the highest rate per hour must be known and usually the highest ten minutes rainfall rate expressed as an hourly rate.

For example, if 4.0 inches fell over that 2.5 hours, nothing says that a rain band did not dump 3 inches in the first hour, (3 inches per hour cumulative) or 0.75 inches in a ten minute period (4.5 inches per hour rate), with the remainder of the storm tapering off to lesser rates. So the average is correct, but the peak hour is much more important for practical purposes.

the half-life of radium-226 is about 1,590 years. How much of a 100mg sample will be left in 500 years

Answers

Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww Xx Yy Zz

I know the best answer ever (*says sarcastically*)

If an article was bought for £400 and was sold for £336 what is the loss persentages

Answers

Answer:

Hey mate!

Here is your answer > >

C.P of an article=Rs.400

S.P.of an article=Rs.336

C.P.> S.P., there is a loss

Loss=C.P.-S.P.

=> Loss=400-336

=Rs.64

Loss%=Loss/C.P.×100

=64/400×100

=16%

Hope it helps!

Thankyou ☆ ☆

Answer: itll be 64

Step-by-step explanation:

dhuiudiSBUVFPVFV WHO CARES WHAT I PUT INHERE

Two airplanes leave the same airport heading different directions. After 2 hours, one airplane has traveled 710 miles and the other has traveled 640 miles. Describe the range of distances that represents how far apart the two airplanes can be at this time

Answers

Answer:

Step-by-step explanation:

710 + 640 = 1350m

Find the commission.
Earning Commission
Sales Commision Rate Commission
$750
9%
?
The commission is $

Answers

Answer:

The commission would be $67.50.

Answer:

$67.50

Step-by-step explanation:

commission amount =  sale price * commission percentage / 100

what is the slope of (0,0) , (3,3)​

Answers

Answer:

The slope is 1

Step-by-step explanation:

[tex]\frac{3-0}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1

|-3| |6|
Secesiones aritméticas

Answers

Answer:

what

Step-by-step explanation:

what

what is the value of x?

3x−6=21?

Answers

Answer:

X = 9

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

What is the value of 4.32 times 10?

Answers

Answer:

43.2

Step-by-step explanation:

4.32 x 10 = 43.2

Answer:

easy

4.320

Step-by-step explanation:

Jamie is painting her house. Each room takes ½ of a liter of paint. If Jamie has 3 liters of paint, how many rooms can she paint? *

Answers

jamie can paint 6 rooms
3 divided by 1/2
3/1 * 2/1
6/1
6

In 1908, W.S. Gossett performed a sleep study on 10 subjects, comparing the number of hours of sleep obtained by each subject with and without (in that order) the application of the drug hyoscyamine. The paired differences d were as follows: 1.0, 0.8, 1.1, 0.1, - 0.1, 4.4, 1.5, 1.6, 4.6, 3.4 At the 1% significance level, is the drug effective in increasing sleep

Answers

Answer:

Since the calculated value of t= 2.8782 does not fall in the critical region so we accept H0 and may conclude that  the drug is not effective in increasing sleep.

Step-by-step explanation:

d              d²

1.0,          1

0.8,         0.64

1.1,           1.21

0.1,          0.01

- 0.1,       0.01

4.4,        19.36

1.5,          2.25

1.6,          2.56

4.6,         21.16

3.4          11.56

∑18.4      ∑59.76

1: We state our null hypothesis  as

H0 : μd= 0     against the claim Ha: μd ≠ 0  

2: The significance level is set at ∝  = 0.01

3: The test statistic under H0 is

        t= d`/ sd /√n

4:The critical region is t ≥ t ( 0.005) 9 = 3.250

5:Computation:

d`= ∑d/n= 18.4/10= 1.84

Sd² = ∑(di- d`)²/n-1 = 1/n-1 [∑di²- (∑di)² /n]

       = 1/9 [59.76 - (18.4)²/10]

        =(59.76 - 33.856)/9

          = 25.904/9

          = 2.8782

6: Conclusion:

Since the calculated value of t= 2.8782 does not fall in the critical region so we accept H0 and may conclude that  the drug is not effective in increasing sleep.

This is because we have taken H0 as the mean of the difference is zero.

This can only be zero when the drug is not effective.

Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest.
45−−√ , 16/5 , −1

Answers

Answer:

I'm assuming 45−−√ is [tex]\sqrt{45}[/tex], and that it belongs to the subset of irrational numbers.

16/5 is a rational number, and -1 is an integer.

All numbers belong to the subset of real numbers.

Step-by-step explanation:

Hope this helped!

Enter the value for x
that makes the equation 16=−4(x−1)+4
true.

Answers

Answer:

-2

Step-by-step explanation:

16=-4x+4+4

16=-4x+8

4x=8-16

4x=-8

x=-2

Tthe required value of x is -2 for which the given expression is true.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
16 = -4(x - 1) + 4
16 - 4 = -4(x - 1)
x - 1 = 12 / -4
x = -3 + 1
x = -2

Thus, the required value of x is -2 for which the given expression is true.

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Bill and Ted are each saving money for a trip to Europe. Bill started with $75 and saves an additional $15 per week. Ted began with $120 and saves an additional $10 per week. After how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer.​

Answers

Answer:

9 weeks

Step-by-step explanation:

After x weeks Bill will save money:

75 + 15x

And Ted will save:

120 + 10x

Since they save same amount, we have equation:

75 + 15x = 120 + 10x15x - 10x = 120 - 755x = 45x = 45/5x = 9 weeks

Would someone like to help me with my math homework and the math is College for Readiness?
I will mark you BRAINLIEST

Answers

Answer:

can i help i need points

Step-by-step explanation:

help i asked this 3 times i will do brainliest no troll answers!

Answers

Answer:

Number two

Exact Form:

11/2

Decimal Form:

5.5

Mixed Number Form:

5

1/2

Step-by-step explanation:

sorry I do not know one hope this helps please mark brainliest

If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of u?

A. u equals p over q
B. u = 1/2s
C. u equals q over p
D. u = 2s

Answers

Answer:

last answer D

i took the test

The expression that most effectively represents u's value would be:

D). u = 2s

What is expression?

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Given that,

In ΔABC,   E is the midpoint in the segment AC and  D is the midpoint of BC.

Now,

CE = 0.5 × AC(midpoint)

CD = 0.5 × CB (midpoint)

Thus,

CE/AC = CD/CB = ED/AB = 1/2        

As ED = s and AB = u

So,  u = 2s    

Learn more about concept  here:

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There are 125 people on a mountain trail. If 55 people on the trail are children, what percentage of the people on the trail are children?

Answers

Answer:

44%

Step-by-step explanation:

.44 x 125 equals 55 n

Answer:

The percentage of people who were children = 44%

Step-by-step explanation:

Total people = 125Children on the trail = 55

We need to determine the percentage of the people on the trail who are children.

All we need is to divide 55 by the total number of people i.e. 125 and then multiply the result by 100.

so

Children percentage = 55 / 125 × 100

                                   = 0.44 × 100

                                   = 44%

Therefore, the percentage of people who were children = 44%

PLZ HELP ME I BEGG YOU

Answers

I got you pinky stinky

Here I will be giving a Brainiest to a good answer :D

Answers

Answer:

A. F

B. D

C. C

D. E

E. G

F. G

G. D

Step-by-step explanation:

Answer: A. 9/4

              C. -1.75

              D. 1.75

              E -2      

              F-1

              -2 1/2  

Step-by-step explanation:

Jackson rides his bike from his home for 30 minutes at a fast pace. He stops to rest for 20 minutes, and then continues riding in the same direction at a slower pace for 30 more minutes. Sketch a graph of the relationship of Jackson’s distance from home over time.

Answers

Answer:

For the first 30 minutes, we will have a line with a given steepness, this will represent the 30 minutes riding at a fast pace.

Then he stops for 20 minutes, we will represent this with a constant line.

Then he again moves for another 30 minutes, but with a slower pace than in the first 30 minutes, then this line will be less steep than the first line.

A sketch of this situation can be seen below.

PLEASE HELP ME!!!!!! Write the information in the table as ordered pairs. Graph the relationship from the table. ​

Answers

Answer:

(3, 60) (5, 100) (8, 160) (9, 180) (12, 240)

Step-by-step explanation:

PLEASE HELP ME !!!
:(

Answers

Answer:

Step-by-step explanation:

G is the incenter of ΔABC,

Incenter of a triangle is defined by the point where angle bisectors of the interior angles intersect.

10). m∠ABG = m∠CBG = 25°

11). m∠BCG = m∠ACG = 18°

  Therefore, m∠BCA = m∠BCG + m∠ACG = 2×18° = 36°

12). m∠ABC + m∠BAC + m∠ACB = 180°

  2(25)° + m∠BAC + 36° = 180°

    m∠BAC = 180° - 86° = 94°

13). m∠BAG = [tex]\frac{1}{2}[/tex](m∠BAC) = 47°

14). Since, incenter is equidistant from all sides of the triangle,

     Therefore, DG = GF = FE = 4 units

15). In right triangle BEG,

     tan(25)° = [tex]\frac{\text{GE}}{\text{BE}}[/tex]

     BE = [tex]\frac{\text{GE}}{\text{tan}25}[/tex]

           = [tex]\frac{4}{\text{tan}25}[/tex]

     BE = 8.6

16). In right triangle BEG,

     cos(25)° = [tex]\frac{\text{4}}{\text{BG}}[/tex]

     BG = [tex]\frac{4}{\text{cos}25}[/tex] = 4.4

17). In right triangle GEC,

    sin(18)° = [tex]\frac{\text{GE}}{\text{GC}}[/tex]

    GC =  [tex]\frac{\text{4}}{\text{sin}(18)}[/tex] = 12.9

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