Mathematics High School

A sequence has the recursive definition of f(1)=2/3, f(n)=f(n-1)×3/2 for n≥2


Right the first five terms of the sequence

Leave answers as fractions

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]f(1)=2/3\\f(2)=f(1)\times (3/2)=(2/3)\times(3/2)=1\\f(3)=f(2)\times (3/2) = 1\times (3/2) = 3/2\\f(4)=f(3)\times (3/2) = (3/2)\times (3/2) = 9/4\\f(5)=(f(4)\times (3/2) = (9/4)\times (3/2) = 27/8[/tex]

So the first five terms are 2/3, 1, 3/2, 9/4, 27/8.

Answer 2

The first five terms are 2/3, 1, 3/2, 9/4, and 27/8 if the  f(1)=2/3, and f(n) = f(n -1)×(3/2); for n ≥ 2.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is given that:

f(1)=2/3,

f(n) = f(n -1)×(3/2); for n ≥ 2

Plug n = 2

f(2) = f(2 -1)×(3/2)

f(2) = f(1)×(3/2)

f(2) = (2/3)(3/2)

f(2) = 1

Similarly;

f(3) = 3/2

f(4) = 94/

f(5) = 27/8

The first five terms are 2/3, 1, 3/2, 9/4, and 27/8.

Thus, the first five terms are 2/3, 1, 3/2, 9/4, and 27/8 if the  f(1)=2/3, and f(n) = f(n -1)×(3/2); for n ≥ 2.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ2

Related Questions

Plz Help!!!!!!
At Suzie’s garden you can exchange vegetables and fruits instead of spending money. If you can exchange 6 cantaloupes for 12 tomatoes, 10 tomatoes for 20 grapes, and 18 grapes for 27 raspberries, how many raspberries could be exchanged for 20 cantaloupes?

Answers

Answer:  20 Cantaloupes will fetch 120 Raspberries.

Step-by-step explanation:

C = Cantaloupes

T = Tomatoes

G = Grapes

R = Raspberries

Conversions (exchange rates):

2T/C

2 G/T

1.5 R/G

Start with 20C

20C*(2T/C) = 40T

40T*(2 G/T) = 80G

80G*(1.5 R/G) = 120R

Hhelp pls lol i don't understand​

Answers

Answer:

m∠1= 80

m∠2= 100

m∠3= 80

Step-by-step explanation:

Given: m∠1= 2x +40

m∠2= 2y +40

m∠3= x +2y

m∠1 +m∠2= 180 (adj. ∠s on a str. line)

2x +40 +2y +40= 180

2x +2y+ 80= 180

2x +2y= 180 -80

2x +2y= 100

2(x +y)= 100

x +y= 100 ÷2

x +y= 50 -----(1)

m∠1= m∠3 (vert. opp. ∠s)

2x +40= x +2y

2x -x +40= 2y

x= 2y -40 -----(2)

Substitute equation (2) into (1):

2y -40 +y= 50

3y= 50 +40

3y= 90

y= 90 ÷3

y= 30

Substitute y= 30 into equation (2):

x= 2(30) -40

x= 60 -40

x= 20

m∠1

= 2x +40

= 2(20) +40

= 40 +40

= 80

m∠2

= 2y +40

= 2(30) +40

= 60 +40

= 100

m∠3

= x +2y

= 20 +2(30)

= 20 +60

= 80

Alternatively, since m∠1= m∠3,

m∠3

= m∠1 (vert. opp. ∠s)

= 80

What is 24 divided by 3072

Answers

Answer:

I might think 124 is the answer

Answer:

128

Step-by-step explanation:

attached..........

PLS HELP I Would really appreciate it

Answers

Step-by-step explanation:

0.376

(In expanded form)

= 0 × 1 + 3 × 1/10 + 7 × 1/100 + 6 × 1/1000

Answer:

0 × 1 + 300 × 1/10 + 70 × 1/100 + 6 × 1/1000

r^2p÷5 ; p = -5, r = - 5​

Answers

Answer:

=-5^2×(-5)÷5

=25×(-5)÷5

=-125÷5

=-25

-91.81 as a mixed number.

Answers

Answer: [tex]-91\frac{81}{100}[/tex]

Step-by-step explanation:

Round the mixed number to the nearest whole or half.

8 4/27 this is a mixed number ok

PLEASE HELP

Answers

Answer:

8 jzhwwh8qoqqnsnwuwjwjqj

Mvhkurgbfssrtgswszc baba burger 56;/3

What is this? I don’t know the answers plz help

Answers

Answer:

a.

Step-by-step explanation:

Not defined

May be iylt help you

Answer:

C

Step-by-step explanation:

Matrices can be multiplied together if the number of columns in the first matrix equals the number of rows in the second matrix.

A is of order (3 × 2) and B of order (2 × 3 )

Since the 2 in the first and the 2 in the second match , the matrices can be multiplied

The resulting matrix is of order (3 × 3 )

This is obtained from the first 3 in order of A and the second 3 in order of B

Then AB is defined and the resultant matrix is of order 3 × 3

PLSSSS HELPPP ITS DUE TODAYYY!!!!!
A ball pit is filled with blue, red and yellow balls as shown in the photo. You reach in and randomly select one ball. Estimate the probability of this ball being yellow

Answers

Step-by-step explanation:

In my opinion I would say about 40% Because you can see 7 red balls on the top and 6 on the bottom. Hope This Helps.

help please, I can't figure these kinds of problems out, and I've just been having a hard time with them.

Answers

Ok relax these kinds of problems just require a bit of understanding. I’ll try my best to walk you through it.
First read each statement carefully.

The term consecutive integers means “whole numbers that follow each other without gaps”
Eg: (1, 2 and 3) or (3,4 and 5) etc.

Now since we don’t know these numbers we can label them as x, (x+1) and (x+2)

Now the question says 2 times the sum of the first and the second is equal to 6 plus the third number

2 times the sum of the first two numbers is
[x + (x+1) ] * 2

6 plus the third number is
6 + (x+2)

Now writing an equation

[x + (x+1) ]*2 = 6 + (x+2)
[2x+1] *2 = 8 + 2
4x + 2 = 10
4x = 8
x= 8/4
x= 2

Now since our three numbers were
x , x+1 and x+2
By plugging in 2 as the value of x we can find out the the three numbers were

2,3 and 4

Please answer this question. Identify the domain and the range of the function, when the functions are (1,0), (3,1), (5,2), (7,3), (9,4). Thank you!

Answers

Step-by-step explanation:

the Domain of the function

=> Df ={1, 3, 5, 7, 9}

the Range of the function

=> Rf ={0, 1, 2, 3, 4}

Domain

set of x values

{1,3,5,7,9}

Range

set of y values

{0,1,2,3,4}

Which point represents the opposite of -2?

Answers

Answer:

2

Step-by-step explanation:

It’s 2 because that the opposite

A water pipe has an outside diameter of 1 1/4 inches and a wall thickness of 5/16 inches. what is the inside diameter of the pipe?

Answers

Answer:

Step-by-step explanation:

There's a small trick here. You have to double the thickness. Why? Because the outside diameter goes through the thickness twice.

Inside diameter = outside diameter - 2 * thickness

outside diameter = 1 1/4 inches

thickness = 5/16

Inside diameter = 1 1/4 - 2 * 5/16

inside diameter = 5/4 - 10/16

Inside diameter = 5/4 - 5/8

Inside diameter = 10/8 - 5/8

Inside diameter = 5/8

4 units to the left of -4 is

Answers

Answer:

-8

Step-by-step explanation:

If you were to do integer operations, then this question algebraically would mean -4-4=-8 because going to the left on a number line is meaning subtraction/negative and going to the right is addition/positve!

Therefore, the answer is -8 :)

please help me im being timed
Find the inverse of the function:

f(x)=−4x+8

Answers

Answer:

(x) = -x/4+2

Step-by-step explanation:

Inverse the function, so swap the places of x and y

x = -4y + 8

Then solve for y

x - 8 = -4y

-x/4 + 2 = y

y = -x/4 + 2

g(x) = -x/4+2

marking brainlist

please helpppp

Answers

Answer:

The answer is AB≠AC

SEMOGA MEMBANTU

please help timed this time i actually added picture
which exponential function is represented by the values in the table​?

Answers

As x increases by 1 the value of f(x) doubles so we need 2^x
When x = 0 the value of f(x) = 3
The correct answer is f(x) = 3(2^x). [the top option]

find the distance between the points (3, 7) and (2, 6)​

Answers

Answer:

1.414214

Step-by-step explanation:

I think this is right lol.

Solve the quadratic equation 3x²-5x=7
Give answer to 3 significant figures

Answers

Answer:

2.57

Step-by-step explanation:

3x²-5x-7=0

Eqn and u will get the answer

please how do I find the answer​

Answers

Answer:

7 of it is 12

Step-by-step explanation:

you have to plus the top ones

Relative to the cave opening, what integer represents the depth of the second
climber?

Answers

Answer:

what is the depth

Step-by-step explanation:

11x - 4 = 20 Solve for x

Answers

Answer:

24/11 approx 2.181818

Step-by-step explanation:

11x -4 = 20

11x= 20 +4

11x = 24

x = 24/11 approx 2.1818181818182

Answer:

x = [tex]\frac{24}{11}[/tex]

Step-by-step explanation:

Given

11x - 4 = 20 ( add 4 to both sides )

11x = 24 ( divide both sides by 11 )

x = [tex]\frac{24}{11}[/tex]

Question in image, please help

Answers

Answer:

34 degrees

Step-by-step explanation:

the verical angle theorem says any two angles opposite of each other from intersecting lines have the same angle

I need 14 and 15 please give me the awnsers

Answers

Answer:

we know brainly.com/question/24497563?answering=true&answeringSource=feedPublic%2FhomePage%2F4

Step-by-step explanation:

[tex]f(x)=x^{4} -x^{3} -7x^{2} +10+5x[/tex]
1. write in standard form
2. use Descartes rule of sign
3. possible roots
4. first synthetic division
5. reconsider possible roots
6. second synthetic division
7. quadratic equation
8. solution set

Answers

Nice hfiebeiciysbwjwkdkcoc

Please help me ASAP

Answers

umm what is this……lol

Type the integer that makes the following division sentence true:

55 ÷ = –5

Answers

the integer is -11, so it’d be 55 divided by -11 equals -5

Help me!! please answer this question with explanation.​

Answers

0.0000679 in scientific notation

[tex]6.79 \times 10 {}^{ - 5} [/tex]

Answer: 6.79×10^-5

Step-by-step explanation:

In order to write the given value in scientific notation, we have to bring the decimal point after the first non-zero digit.

So it will become 6.79

Now for the zeros that have been removed we represent them in the form 10^-5.

And it is -5 because we have removed the zeros from the left side of the value. The 10^-5 indicates that we have to move "five points" to the "left side" to get the original value again.

So it is first, 0.0000679

(we make the decimal point jump across four zeros to the right side and then across the 6 which is the first non zero digit, that is 5 jumps in total as indicated by the 10^-5)

Then it becomes:

6.79×10^-5

The speed of light is approximately 300,000 kilometers per second. How many miles does light travel in an hour?​

Answers

Answer:

671080887.6

Step-by-step explanation:

1 second = 300,000km

3600 seconds = 3600 x 300,000 = 1080000000 km then convert to miles

is 671080887.6

Name 3 planes parallel to FL

Answers

Answer:

I have answered. it is perfect answer

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