How do you write a recursive formula

Answers

Answer 1

You need to show how a term of formula is based on a previous term.

For example, let's say you have the sequence 3, 6, 9, 12, ...
(multiples of 3).

As a regular function, you can have y = 3x, for the domain of all integers greater than 0. Since the domain is 1, 2, 3, 4, ..., when you multiply those numbers by 3, to get y, you generate the sequence.

To define the sequence recursively, you must base each new number on the previous number.

Start by stating the first term.

a1 = 3

If you look at the sequence, 3, 6, 9, ..., you see it has a constant difference, and it is an arithmetic sequence, so to generate a term, you need to add 3 to the previous term.

Once we defined the first term to be 3, the next term is a2 = 3 + 3 = 6
Then a3 = 6 + 3 = 9, etc.

To define the sequence recursively, just generalize the addition of 3 to a term to get the next term.

[tex] a_{1} = 3 a_{n} = 3 a_{n - 1} [/tex]

Related Questions

Which is an inccorect rounding of 53.864

Answers

from your options the answer is 50.

according to the law of conservation of energy, when a car uses 10,000J chemical energy from gasoline, how much energy will be transformed into sound,heat,and mechanical energy.

Answers

According to the Law of Conservation, 10,000 J of energy will be released and transformed into sound, heat, and mechanical energy. This is true because energy cannot be destroyed or created; it just transforms into some other type of energy.

Hope this helps!

What is the median and mode

Answers

Median is the middle number

60, 60, 65, 70, 70, 85, 90

70 is your median

mode is the number(s) that show up the most
60 and 70 is your mode, since they show up twice (one more than the others)

Range is largest number minus the smallest
90 - 60 = 30, 30 is your range

Mean is all the numbers added together divided by the number of numbers there are
60 + 90 + 65 + 70 + 70 + 85 + 60 = 500
500/7 = 71.42
Mean = 71.42

hope this helps

Let a and b stand for two different rational numbers. If |a| > |b| then what else must be true?

Answers

a is farther from 0 then b is

The sun produces 3.8x10^27 joules of energy per second. How much energy is produced in a year? (Note: a year is approximately 31,000,000 seconds.) Put it in scientific form.

Answers

If you're talking about the 'scientific notation', the answer would be (3.800000000000000000000000000, 26 zeroes.)

Answer: About [tex]\approx1.178\times10^{35}[/tex]

Step-by-step explanation:

Given : The sun produces[tex]3.8\times10^27[/tex] joules of energy per second.

It is also given that a year is approximately 31,000,000 seconds.

In scientific notation , it can be written as [tex]3.1\times10^7[/tex]

Then , the amount of energy is produced in a year will be :-

[tex]3.8\times10^{27}\times3.1\times\times10^7\\\\=3.8\times3.1\times10^{27}\times10^7\\\\=11.78\times10^{27+7}\\\\=11.78\times10^{34}=1.178\times10^{35}[/tex]

Hence, the amount of energy is produced in a year [tex]\approx1.178\times10^{35}[/tex]

Please, please help!

Two straight lengths of wire are placed on the ground forming vertical angels if the measure of one of the angles formed is 72 degrees, what are the measures of the other three angles? Explain your answer.

Answers

They need to add to 180 degrees

108 * 72 = 108 degrees

Jenna read 25 pages of a book in 30 minutes at the same rate how many pages can she read in 3 hours

Answers

• Convert 3 hours into minutes: 3 x 60(minutes in an hour) = 180 minutes
• Divide to see how many times 30 minutes goes into 180: 180 ÷ 30 = 6
• Multiply: 25 x 6 = 150

So, Jenna can read 150 pages of a book in 3 hours. Hope this helps! :D

~PutarPotato

Can 9/12 be simplified

Answers

yes.

9/12 can be simplified to 3/4

(divide by 3 top & bottom)

hope this helps

Yes they can. When it comes to simplifying fractions, whatever you do to the numerator, you must do to the denominator. With this fraction, we can divide both the top and bottom by 3 to get 3/4. 9/12 is 3/4 in simplest form.

How do you write 5.8 as a percentage

Answers

Multiply 5.8 by 100 to convert to percent:

5.8 × 100 = 580 %

580%, hope this helps!

Doug dives from a platform that is 5 meters above water. His dive takes him 2.6 meters below the surface of the water. How far does Doug's dive take him?

Answers

The total distance Doug dives from the platform to the under the water is 7.6 meters.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Doug dives from a platform that is 5 meters above the water.

His dive takes him 2.6 meters below the surface of the water.

∴ To find the total distance Doug dived we have to sum the height of the platform above water and the distance which he dived below the water,

= (5 + 2.6) meters.

= 7.6 meters.

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Quadrilateral ACEG≅ Quadrilateral MNPR

Which statement is true?

Answers

Line CE is congruent to line NP is the true statement.

it total revenue is $3000, cost of goods is $1500, and total selling expenses is $500 what is the Profit for the business

Answers

$3000- $1500= ?... ?- $500= your answer
Hope this helped if you need more help let me know and i will explain more

Hello!

To find your answer, you simply need to subtract:

3000 - 1500 = 1500

1500 - 500 = 1000

So, the profit for the business is $1000.

I hope this helped you! :)

25% of all the seats in the auditorium is 37 shares the total number of seats in the auditorium is

Answers

The number of seats in the first row is 18;
The number of seats in the second row is 18+2=20;
The number of seats in the third row is 18+2*2=22;
The number of seats in the fourth row is 18+3*2=24;
...
The number of seats in the nth row is 18+(n-1)*2.

Notice that if we knew the total number of rows we would be able to sum the number of seats in each row and get the total number of seats.

(1) The number of rows of seats in the auditorium is 27. Sufficient.
(2) The number of seats in the last row is 70 --> 18+(n-1)*2=70, where n is the number of rows. We can get n. Sufficient.

Answer: D.

120% of 33 is what number?

Answers

Change 120% into a decimal using the DP rule. D stands for decimal and P stands for percent. If you are trying to change a percent into a decimal then move the decimal spots two spaces to the right, but if you are changing a decimal into a percent then you move the decimal two spaces to the right. In this case we have to move the decimal two spaces to the left. Imagine in a percent that there is an imaginary decimal on the right of the 0 in 120 so when you move the decimal to the left it will become 1.20. Now multiply 1.20 and 33 which should give you an answer of 39.6 .

The answer is simply 39.6

What is an intersection point?

Answers

An intersection point is a point where two lines meet.

A point on a on two lines that are on the same plane that pass through each other
hope this helps

An architect makes a blueprint with a scale of one fourth inch equals 2 ft. Which will be the dimensions of the drawing of a warehouse room measuring 60 ft by 100 ft? Answer Options with 5 options A. 15 inches ''by 25 inches '' B. 7.5 inches ''by 12.5 inches '' C. 120 inches ''by 200 inches '' D. 480 inches ''by 800 inches '' E. 30 inches ''by 50 inches ''

Answers

Facts: scale .25"=2'
room 60'×100'

Equation: 60/2=30×.25=7.5
100/2=50×.25=10.5

Answer: B

The new dimension in inches is 7.5 inches by 12.45 inches. Hence, option B is correct.

What is ratio?

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.

As per the given information in the question,

One fourth inch equal to 2ft.

Mathematically,

1/4 inch = 2ft

0.25 inch = 2ft

The given dimensions are 60 ft by 100 ft.

Now,

0.25 inch = 2ft

x inch = 60 ft

2x = (0.25 × 60)

x = 15/2

x = 7.5 inches

Then,

0.25 inch = 2ft

y inch = 100 ft

2y = 100 × 0.25

y = 25/2

y = 12.45 inches

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create a slope that will be parallel to the slope provided which is 5/9 what is the parallel slope?

Answers

parallel lines have the same slope so 5/9 would be the answer

Answer:

The parallel slope would be 5/9

Step-by-step explanation:

Parallel lines have the same slope. So, if the original line had a slope of 5/9, the new line would also have that slope.

Denise provides water for the runners at her schools 10K road race. She has a container that holds 678 ounces of water. How many 8-ounce cups can she fill with water?__________cups

Answers

divide total ounces by the amount each cup can hold

678 / 8 = 84.75

so they can fill 84 cups

678 oz/ 8 = # of cups she can fill

678/8 = 84.75

She can fill 84 cups

hope this helps

You eat 3 8 of a pie and your sister eats 1 4 of the pie. Explain who ate more of the pie

Answers

First, you need to find a common denominator, you should get 2/8 and 3/8. So, you ate more of the pie

You ate more of the pie, the reason this is the case is because you ate 1.5 fourths of the pie. In order to solve these types of problems, you need to make the divisors of the amount of the pie you ate the same. in order to do this, we need to make 8 become 4, to do this we need to divide 8 by 2 which gives us four, remember what you do to the top of the fraction you MUST do to the bottom, which means that we need to divide the bottom by 2 which gives us 1.5.
We could also make the divisor of the fraction that expresses the amount of pie your sister ate 8 instead of making the other divisor 4. In order to do this, we must multiply 4 by 2 to give us 8, remember what we do to the top of the fraction you MUST do to the bottom, so we multiply the bottom by 2 giving us 2/8. You ate 1.5/4 and your sister ate 1/4 or your sister ate 2/8 and you ate 3/8. You ate more of the pie. I hope that this helped you out.

What is the value of p? 0.6441−(−0.29)=p

Answers

the value of P= 0.9341

Answer: p = 0.9341

Have a good day!

Suppose △PKN≅△BGH△PKN≅△BGH. Which other congruency statements are correct? Select each correct answer. △NKP≅△HBG△NKP≅△HBG △KPN≅△BHG△KPN≅△BHG △NPK≅△HBG△NPK≅△HBG △KNP≅△GHB

Answers

Answer:

△NPK≅△HBG; and △KNP≅△GHB

Explanation:

Using the given congruence statement, we can determine corresponding pieces of the triangles:

P corresponds to B; K corresponds to G; and N corresponds to H.

This means that △NKP≅△HGB, not HBG.

△KPN≅△GBH, not BHG.

△NPK≅△HBG; this is correct.

△KNP≅△GHB; this is correct.

Answer: k12 answers have a nice day!!!

Step-by-step explanation:

Diana's painting statue she has 7/8 of a gallon of paint remaining each student requires 1/16 of a gallon of paint how many statues can she paint

Answers

Easy, first turn the factions into deciamls, then so 1.16-7.8=6.64. So, 6.64

What is 2 (1/3) — -3 (2/3) = ?

Answers

2 (1/3) - -3 (2/3) = 6

I hope this helped you! c:

A piece of carpet is 8 feet wide and 12 feet long. The carpet needs to be reduced by a scale factor so that the reduced carpet is 2 feet wide. What is the area of the reduced carpet

Answers

6 feet because 8 / 12 reduces to 2 / 3 and you multiply 2 times 3

Hi there.

So, we've got the dimensions.

l = 12, w = 8

We know that the width has been divided by 4. That means we also divide the length by 4. This gives us the new dimensions of:

l = 3, w = 2

A = lw

3 · 2 = 6 ft²

Cheers~

Nathan and Sydney start out together on a bike trail that is 24 miles long. Nathan bikes at 88 miles per hour while Sydney bikes at 12 miles per hour. Which statement is true?

Answers

sydney is true because the bike trail is no longer than 24 miles

Sydney is true because 88 miles is longer than 24 miles

What is the value of 48x +35. When x=2

Answers

48x + 35
x = 2
plug in 2 for x
48(2) + 35
multiply 2 and 48 together
48 x 2 = 96
add the product (96) with 35
96 + 35 = 131
answer is 131

131 is your answer

hope this helps

48x + 35 = ?
48 x 2 + 35
96 + 35 =
131
I hope this helps
Please make me brainliest

what is 4018 divide by 82

Answers

the answer is of 4018 divided by 82 is 49

4018 / 82 = 49

Hope this helps

is the product of a fraction less than 1 and a whole number greater than or less than the whole number? explain

Answers

It depends, if the numerator is greater than the denominator, the product will be greater. If not, the product will be less than the whole number. If the fraction is equal to one,(ex. 2/2,50/50,-2/-2), then it would be equal.

Multiplying a fraction less than 1 with a whole number produces a result that is less than the original whole number because you are taking a portion of it.

The product of a fraction less than 1 and a whole number is always less than the original whole number. To understand why, consider the fraction as a part of the whole. If you multiply the whole by a part less than the whole (a fraction less than 1), you're essentially taking only a portion of it, which must logically be smaller than the whole itself.

Carmen, Reuben, and Bob have a total of $133 in their wallets. Bob has 3 times what Reuben has. Carmen has $8 more than Reuben. How much does each have?

Answers

So you will want to form a few equations. The first one is:
C+R+B=133
Then you will want to form an equation for Bob:
B=3R
Then, another for Carmen
C=R+8

Knowing this information, you can plug each in, solving for R.

R+8+R+3R=133      Now Solve
5R+8=133               Subtract 8 from both sides
5R=125                   Divide 5 from both sides
R=25                       Now substitute R in for Carmen and Bob equations.

R=25                        Reuben has $25
C=8+25                    Add
C=33                        Carmen has $33
B=3(25)                    Multiply
B=75                        Bob has $75

Check answer:

25+33+75=133
133=133

I hope this helps!

Simplify the following expression by combining like terms: 2x⋅2x⋅7x

11x

4x+7x

28x3

28x

Answers

The correct answer would be C.

28x^3

Hopefully this Helped!:)

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