Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12.

Which explicit formula can be used to model the same sequence?

f(x) = 12(4)x
f(x) = 3(4)x − 1
f(x) = 4(12)x
f(x) = 4(3)x − 1

Answers

Answer 1

Answer:

B

Step-by-step explanation:

I got u

Answer 2

The explicit formula for the geometric progression is f ( x ) = 3 ( 4 )ˣ⁻¹

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

f ( x + 1 ) = 4 f ( x )

where the second term is a₂ = 12

Now , the explicit formula is given by

f ( x ) = 3 ( 4 )ˣ⁻¹

when x = 2

f ( 2 ) = 3 ( 4 )²⁻¹

f ( 2 ) = 3 ( 4 )

f ( 2 ) = 12

Hence , the GP is f ( x ) = 3 ( 4 )ˣ⁻¹

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Related Questions

Determine which is the better buy
1 kilogram of bananas for $2.06 or 4 kilogram of bananas for $7.48
PLZ EXPLAIN PLZ

Answers

Answer: 4 kilograms of bananas for $7.48

Step-by-step explanation:

Unit price for 1 kilo= $2.06

2.06 x 4 = 8.24

Unit price for 4 kilo= $1.87

2.06 > 1.87

So, 4 kilograms of bananas is the better buy.

Simple form:

Answer 1: 2.06

Answer 2: 1.87

Answer 3: greater than

Answer 4: 4 kilograms of bananas for $7.48

Ben flew his small airplane 660 km in 6 hours flying with the wind. He flew 350 km against the
wind in 7 hours. Find the rate at which he flew in still air and the rate of the wind.

Answers

Answer:

r = 80 KM/HR

w= 30 CM/HR

Step-by-step explanation:

16 .Write an equation that represents the statement
below.
"Twelve less than a number, x, is 18."

Answers

Answer:

x-12=18

Step-by-step explanation:

Answer: if X = 30, then the equation is 30 - 12 = 18

pH = -log10 (C).
What is the value of c when the acidity of the liquid solution is 5 pH units?
OA. – 510
B. 5-10
OC. – 105
D. 10-5

Answers

B, 5-10 is right I believe

I don’t get this Need help asap

Answers

Answer:

Step-by-step explanation:

x - 2y =8

   -2y = -x + 8

      [tex]y = \frac{-1}{-2}x+ \frac{8}{-2}\\\\y =\frac{1}{2}x - 4[/tex]

When x = 4,

     [tex]y = \frac{1}{2}*4-4\\\\ = 2-4\\\\y = -2[/tex]

(4, - 2)

When x = -4,

    [tex]y =\frac{1}{2}*(-4) - 4\\\\ = -2 - 4\\\\= - 6[/tex]

(-4, -6)

Plot the points (4, -2) and (-4 , -6) in the graph and Join the points

i need helppp could you help please pl,s pls pls pls pls pls plks pls pls pls pls pls pls

Answers

Answer:(-4,6)

Step-by-step explanation:

you go down four then over six and you find the letter F

Answer:

(6, -4)

Step-by-step explanation:

x axis is before the y axis

SOMEONE PLSS HELP ASAP

Answers

The answer is most likely 8.

0.7k − 1.6 ÷ 2 − 5.2 = 1.7 − 0.7

Answers

your answer is k=10 the step by step is kn the picture

Guys can u help me please

Answers

Answer:

the first one is 5 times 5 times 5

the second is 7 times 7

the third is 2 times 2 times 2

Step-by-step explanation:

5x5x57x72x2x2

A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component.
Receiver: Kenwood, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Turntable: Onkyo, Sony, Teac, Technics
A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules:
A. In how many ways can one component of each type beselected?
B. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
C. In how many ways can components be selected if noneis to be sony?
D. In how many ways can a selection be made if at leastone sony component is to be included?
E. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component?

Answers

Answer:

Step-by-step explanation:

A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component.

Receiver: Kenwood, Sony, Sherwood

Compact disc player: Onkyo, Pioneer, Sony, Technics

Speakers: Boston, Infinity, Polk

Turntable: Onkyo, Sony, Teac, Technics

A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules:

A. In how many ways can one component of each type beselected?

B. In how many ways can components be selected if boththe receiver and the cd player are to be sony?

C. In how many ways can components be selected if noneis to be sony?

D. In how many ways can a selection be made if at leastone sony component is to be included?

E. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component?

Please help I need by Tomorrow!

Answers

Answer:

[tex]f(a) = 5a + 1[/tex]

[tex]f(a + h) = 5a + 5h +1[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x + 1[/tex]

Solving (a): f(a)

Substitute a for x in [tex]f(x) = 5x + 1[/tex]

[tex]f(a) = 5a + 1[/tex]

Solving (b): f(a + h)

Substitute a + h for x in [tex]f(x) = 5x + 1[/tex]

[tex]f(a + h) = 5(a + h) +1[/tex]

Open bracket

[tex]f(a + h) = 5a + 5h +1[/tex]

Solving (c): [tex]\frac{f(a + h) - f(a)}{h}[/tex]

In (a):

[tex]f(a) = 5a + 1[/tex]

In (b):

[tex]f(a + h) = 5a + 5h +1[/tex]

So:

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - (5a+1)}{h}[/tex]

Open bracket

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - 5a-1}{h}[/tex]

Collect Like Terms

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a- 5a+5h+1 -1}{h}[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5h}{h}[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]


5th grade math. Correct answer will be marked brainliest.

Answers

Answer:

part a is 3500

Step-by-step explanation:

i need help.........

Answers

Answer:

17

Step-by-step explanation:

What is the value of y?
What is the area, in square inches, of the rectangle

Answers

Answer:

Part A:  y = 3

Part B:  Area = 60 sq units

Step-by-step explanation:

we can create this system of equations from the information given:

8y + 2x = 34

10y + 2x = 40

now we can subtract to get:

-2y = -6

y = 3

solve for 'x':

8(3) + 2x = 34

24 + 2x = 34

2x = 10

x = 5

Area of Rectangle is 12 x 5

WILL GIVE BRAINLIEST, 100 POINTS
The diagram shows a 6 ft student standing near a tree. The shadow of the student and the shadow of the tree end at point A. What is the height of the tree?

Question 1 options:

90 ft^2

90 ft

18 ft

18 ft^2

Answers

Answer:

18ft

Step-by-step explanation:

:p

The height of the tree is 14 feet.

What is Proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Height of Man= 6 feet

Shadow height= 5 feet

and, Height of tree shadow= 15 feet

So, using Proportion

FE/ BC = FA/ AC

6 / x = 5 / 15

5x= 90

x= 14 feet

Hence, the tree is 14 feet tall.

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PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

PLS SHOW THE WORK!!!!!!!!

Answers

Answer:

1. x = - 1 -y over 2

2. x = -4(2+y) over 3

Step-by-step explanation:

Answer:

1. x = - 1 -y over 2

2. x = -4(2+y) over 3

:)

what is the surface area of this shape ?

Answers

Answer:

what is the surface area of this shape? 328 yd

Step-by-step explanation:

Surface area = 2 × (11×8 + 11×4 + 8×4)

Surface area = 2 × (88 + 44 + 32)

Surface area = 2 × 164

Surface area = 328 yd

Jamie can paint a wall in 54 minutes Together Connie and Jamie can paint the same wall in 36 minutes How long would it take Connie to paint the same wall by herself

Answers

Answer:

The answer is 108

Step-by-step explanation:

I did this for my exam got 100

Together they can paint 5/108 of a wall in 1 minute.  So they can paint the entire wall in 108 minutes.

We have given that,

John can paint 1/54 of a wall in 1 minute.

James can paint 1/36 of a wall in 1 minute.

What is the formula for total wall paint in one minute?

Total wall paint  of both in one minute is calculated by adding the both the paint in one minute it gives us the total paint in one minute

Therefore ,total wall paint in one minute =1/54 + 1/36

So if they work together, they can both paint 1/54 + 1/36 of a wall in 1 minute.

1/54 + 1/36 = 2/108 + 3/108 = 5/108 = 0.04629.

Therefore,together they can paint 5/108 of a wall in 1 minute.  So they can paint the entire wall in 108 minutes.

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What are the slope and Y intercept of Y≥-2x+3

Answers

slope is -2x and the y intercept is 3
y=mx+b (m = the slope) (b = the y intercept)

hope this helped

5) The diagram below shows a ramp connecting the ground
to a loading platform 4.5 feet above the ground. The ramp
measures 11.75 feet from the ground to the loading
platform. What is the angle of elevation formed by the
ramp and the ground to the nearest degree?

Answers

Step-by-step explanation:

///////hope it helps:)

The trigonometric function gives the ratio of different sides of a right-angle triangle. The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse.

What is Sine (Sinθ)?

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

The angle of elevation is equal to,

The angle of elevation = Sin⁻¹ (4.5/11.75)

                                      = 22.5183° ≈ 23°

Hence, the angle of elevation formed by the ramp by the ground to the nearest degree is 23°.

Learn more about Sine:

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find x and round to the nearest tenth

Answers

Answer and Step-by-step explanation:

22ft = x (c)

20ft = y (b)

18ft = z (a)

Plug into equation.

[tex]22^{2} = 20^{2} + 18^{2} - 2(20)(18)cosC (X)\\\\484 = 724 - 720cosC\\\\-240 = -720cosC\\\\\frac{1}{3} = cosC\\\\cosx^{1} (\frac{1}{3} ) = C\\\\C = 70.5288\\\\[/tex]

C ≈ 70.5 is the answer.

Chicken costs $3.20 per pound, and beef costs $4.59 per pound. What is the exact cost of 3 pounds of chicken?

Answers

Answer:

$9.60

Step-by-step explanation:

3.20x3=9.60

Some one please help me on this I am very much dum

Answers

I don’t know this one either bro

Please answer the question and explain your answer. I will be marking brainiest with the correct answer and best explanation.

Answers

Answer:

28.26

Step-by-step explanation:

A = r^2

So the equation is. Area of circle = pi(3.14) * radius(3) to the power of 2 (^2)

A = 3.14(3)^2

A = 3.14(9)

A = 28.26

what is 3/5 + 3/2 ?
I’ll mark as BRAINLIEST

Answers

Answer:

2 1/10

Step-by-step explanation:

Cheese Or Pickles? WILL GIVE BRAINLIEST

Answers

Answer:

Pickles. My friends are allergic to cheese.

Can I please get the answer ?

Answers

Answer:

The sign depends on the sign of the larger number.

A recipe requires one quarter cup of milk as a base and then, In addition, 1 cup of milk for every 4 cups of flour. Choose a linear equation that describes the relations.

Answers

Answer:

Step-by-step explanation:

Where are the choices?

m and f are the cups of milk and flour, respectively.

m = ¼f + 1

Chloe has $15 to spend on pencils. Each box of pencils costs $2. How many
boxes of pencils can Chloe have buy? How much money will she have left
after she buys the pencils?

Answers

Chloe can buy 7 pencil boxes and have 1 dollar left

10.Suppose that you have bought 3 large glass-fronted cabinets. You have three workers, A, B and C, to help you with transporting the cabinets from the furniture store to your home, and you want them to finish it in (at most) one trip each. From past experience, it is known that the probability that A breaks something in a given trip is 10%, the probability that B breaks something in a given trip is 15%, and the probability that C breaks something in a given trip is 20%. The events that A, B, or C breaks something in a given trip are independent of each other. You come up with three strategies: (a) A transports all the furniture, (b) A transports two cabinets and B transports one cabinet, or (c)

Answers

Answer:

Step-by-step explanation:

To find the expected no of broken cabinets for each strategy.

If A transport all the furniture

Suppose X₁ = number of furniture A broken

X₁ follows a binomial with n = 3, p = 0.10

E(X₁) = np

E(X₁) = 3 × 0.1

E(X₁) = 0.3

If A transport two (2) cabinets & B transport one (1) cabinet

expected no. of the broken cabinet by A out of 2 is

= 2 × 0.1

= 0.2

Suppose X₂ denotes the no of broken furniture by B

E(X₂) = np

where n= 1 and p = 0.15

E(X₂) = np

E(X₂) = 1 × 0.15

E(X₂) = 0.15

Thus. the expected number of broken cabinets = 0.2 + 0.15 = 0.35

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