f(3) = 12 for a geometric sequence that is defined

recursively by the formula f(n) = 0.5 ∙ f(n – 1), where

n is an integer and n > 0.

Write the equation in explicit form.



Answers

Answer 1

Answer:

[tex]f(n) = 96 * 0.5^n[/tex]

Step-by-step explanation:

Given

[tex]f(3) = 12[/tex]

[tex]f(n) = 0.5 * f(n-1)[/tex]

Required

Write as an explicit function

When n = 3, we have:

[tex]f(3) = 12[/tex]

[tex]f(3) = 0.5 * f(3-1)[/tex]

[tex]f(3) = 0.5 * f(2)[/tex]

Substitute: [tex]f(3) = 12[/tex]

[tex]12 = 0.5 * f(2)[/tex]

Solve for f(2)

[tex]f(2) = 12/0.5[/tex]

[tex]f(2) = 24[/tex]

So, we have;

[tex]f(3) = 12[/tex]

[tex]f(2) = 24[/tex]

Since it is a geometric sequence, calculate the common ratio (r)

[tex]r = \frac{f(3)}{f(2)}[/tex]

[tex]r = \frac{12}{24}[/tex]

[tex]r = 0.5[/tex]

Calculate the first term using:

[tex]r = \frac{f(2)}{f(1)}[/tex]

Solve for f(1)

[tex]f(1) = \frac{f(2)}{r}[/tex]

[tex]f(1) = \frac{24}{0.5}[/tex]

[tex]f(1) = 48[/tex]

The explicit function is then calculated as:

[tex]f(n) = f(1) * r^{n-1[/tex] ----nth term of a gp

[tex]f(n) = 48 * 0.5^{n-1[/tex]

Split the exponent

[tex]f(n) = 48 * \frac{0.5^n}{0.5^1}[/tex]

[tex]f(n) = 48 * \frac{0.5^n}{0.5}[/tex]

[tex]f(n) = 96 * 0.5^n[/tex]


Related Questions

Hey guys. So I'm doing a basic program for a battle game in Javascript, and I've having trouble on this one question. (subtraction)

If I have one number like 20, then 3 numbers such as 2, 4 and 7, I could easily find out which number in those 3 i subtracted by. For example if I had 18 as the answer, then I could do 20 - 18 and get 2 from the 3 numbers.

But how do I do that twice? or three or more after that one time? how would I know which one I picked after? (after the number is used once, it can still be used forever on, it's always random)

Answers

Answer:

can i show you how to do it

Step-by-step explanation:

What is the value of x? NEDD HELP ASP

A x=15

B x=30

C x=37.5

D x=52.5

Answers

Answer:

The value of x is 15 .

Option (A) is correct.

Step-by-step explanation:

As given

∠1 and ∠2 are complementary.

i.e the sum of ∠1 and ∠2 is 90° .

Thus

∠1 + ∠2 = 90°

x° + (3x+30)° = 90°

x + 3x + 30 = 90

4x = 90-30

4x = 60

x = \frac{60}{4}x=

4

60

x = 15

Therefore the value of x is 15 .

Option (A) is correct.

Answer:

A. x=15

Step-by-step explanation:

To solve this problem, we can combine like terms.

3x + (1)x are like terms.

3x + (1)x = 4x.

Since 3x and (1)x are the only pair of like terms, we are done with this step.

Complementary angles have a sum of 90°.

4x + 30 = 90.

Next, we subtract 30 from 90.

90 - 30 = 60.

Then, we divide 60 from 4.

60 / 4 = 15.

15 is the final answer.

Therefore, the value of x is 15.

If Jeff is a manager at the local movie theatre, his annual salary is $46,000 and his company gives a 1.5% raise each year. What will be the total amount of money Jeff earns in 4 years assuming he gets the raise each year?

Answers

Answer:

59000

Step-by-step explanation: yep

Which set of data points could be modeled by a line of best fit that is a decreasing linear function?
A. {(0, 0), (1, 8), (2, 15), (3, 22), (4, 30)}
B. {(0, 5), (1, 6), (2, 10), (3, 16), (4, 28)}
C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}
D. {(0, 64), (1, 60), (2, 52), (3, 39), (4, 22)}

Answers

Answer:

c I do believe

Step-by-step explanation:

can you help me with this question is the correct answer b

It’s C becausw if u

Explanation:

Answer: thx pass some points !

Evaluate the function for an input value of 3. f(x)= −4x 2 −3x−5

Answers

Answer:

- 50

Step-by-step explanation:

x = 3

f ( x ) = - 4x^2 - 3x - 5

f ( 3 )

= - 4 ( 3 )^2 - 3 ( 3 ) - 5

= - 4 ( 9 ) - 3 ( 3 ) - 5

= - 36 - 9 - 5

= - 50

Plz help fast will mark brainliest!!!

Answers

Answer:

V≈523.6

Step-by-step explanation:

yes or no? help me out thank you so much whoever does:))

Answers

yes. i’m not for sure.

Answer:

Yes

Step-by-step explanation:

The bottom left corner is a right angle

Please help I’m so stressed over this ok here it is it cost $12.50 to enter an amusement park and $1.50 to play each game. Solve an inequality to find the number of games, g, Cole can play if he has $35 to spend at the park. Enter your answer in the box.

Answers

Answer:
He can go on 15 gams

which number lies half-way between 356 and 1025​

Answers

Answer is 695

(365+1025)/2= 695

There are 8 sophomores on the academic team. At the last competition, they each took the math test. Their scores were 82%, 92%, 76%, 72%, 92%, 74%, 80%, and 78%. What was the median math score of the sophomores? 79% 82% 87% 92%

Answers

The median of the math scores is = 79%.

You can understand more about calculation of median of a set of numbers below.

Estimation of median scores

The total number of sophomores is = 8

The percentage score of each sophomore = 82%, 92%, 76%, 72%, 92%, 74%, 80%, and 78%.

To calculate the median of the percentage scores, arrange the scores in ascending order and pick the figure in the middle as the median math score.

72, 74, 76, 78, 80, 82, 92, 92

Here the median is two figures 78, and 80 which are located in the middle. The median is =>78 +80/2

= 158/2 = 79%

Therefore, the median of the math scores is = 79%

Learn more about median calculation here:

https://brainly.com/question/14532771

-----------------------

A. 79%

edge 2022 :)

------------------------

In ADEF, the measure of measure of ZD to the nearest degree.
E
52
X
F
D
14

Answers

Answer:

74 degrees

Step-by-step explanation:

Assuming we have the following

FD = 14

DE = 52

m<F = 90degrees

Required

m<D

DE = hypotenuse

FD = adjacent

Using the SOH CAH TOA identity

Cos m<D = adj/hyp

Cos m<D = 14/52

m<D = arccos(0.2692)

m<D = 74.38

m<D to the nearest degree is 74degrees

A banana split costs $2.50. A milkshake costs $1.70. Bobby,Jack, and Ted ordered one of each and split the cost. How much does each boy owe?

Answers

Answer:

$4.20

2.50+1.70=4.20

Answer:

Jack= $4.20

Bobby=$4.20

Ted=$4.20

Step-by-step explanation: This is the answer because if you add up all the drinks the total they payed is $12.60 so you just divided that by how many people there are and get $4.20

1,2,5 please I don’t really understand this lesson :(:/
AKA 1,2,5 only!

Answers

Answer:

Step-by-step explanation:

Volume of a triangular pyramid = [tex]\frac{1}{3}(\text{Area of the triangular base})(\text{Height})[/tex]

1). Volume of the pyramid = [tex]\frac{1}{3}(72)(15)[/tex]

                                           = 360 cm³

2). Volume of the pyramid = [tex]\frac{1}{3}(\text{Area of the triangular base})(\text{Height})[/tex]

   Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]

                                                 = [tex]\frac{1}{2}(8)(5)[/tex]

                                                 = 20 cm²

   Therefore, volume of the pyramid = [tex]\frac{1}{3}(20)(12)[/tex]

                                                             = 80 cm³

5). Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

    Here, r = radius of the circular base

    h = Height of the cone

    Volume of the cone = [tex]\frac{1}{3}\pi (2)^2(4)[/tex]

                                      = [tex]\frac{16\pi }{3}[/tex]

                                      = 16.76 cm³

HELP ME PLEASEEEE NO LINKS OR IMMA REPORT WORTH 15 POINTS

Answer choices are

1.The same or diffrent, diffrent

2. Corresponding angles, the complementary to a corresponding angle, The supplementary to a corresponding angle, The vertical angle to a corresponding angle, they are not corresponding in anyway

Answers

Answer: 1=same

Step-by-step explanation: because if you line them up they are all the same size

HELP ME PLEASE!! ILL MARK BRAINLIEST FOR THE FIRST TO AMSWER ! BUT THE ANSWER AS TI BE RELATED TO THE QUESTION CAUSE IF NOT I WOMT MARK U BRAINLIEST !​

Answers

C is your will be your answer

please help


Will mark brainlist

Answers

I think answer is b that is 10raise to 2

can someone please help with this? real answer only please......ive asked multiple questions today becuz i dont really understand the assignment, please help​

Answers

i believe the answer is A

3-108. Write an equation and find the answer for each of the following problems. Give answers in decimal form. Homework Help a. What is the product of three tenths and four hundredths?​

Answers

product means multiply, so 3/10 * 4/100 = 12/1000, simplified is 6/500

Marsha deposited 7500 into a savings account 5 years ago. The simple interest rate is 3%. How much money did Marsha earn in interest

Answers

Answer: $1125

Step-by-step explanation: 7500 x 3%=  225   Then multiply 225 by the 5 years. You will then get 1125.  Marsha earned $1,125 in interest.

I hoped this helped, have a great rest of your day!

Answer:

$1125

Step-by-step explanation:

plz crown

Para reformar la cocina de su caja Berta compro la semana pasada 2 cajas de plaquetas para el suelo y 4 de azulejos para la pared por 200 €. Hoy la comprado 2 cajas más de plaquetas y otras 2 de azulejos per 130 € Cuanto cuesta la caja de plaquetas y la de azulejos

Answers

Answer:

Caja de plaquetas = x = 30 €

Caja de azulejos = y = 35 €

Step-by-step explanation:

Deje que el costo de

Caja de plaquetas = x

Cuadro de mosaico = y

Por Berta

Para reformar su cocina, Berta compró la semana pasada 2 cajas de baldosas de plaquetas para el suelo y 4 cajas de baldosas para la pared por 200 €.

2x + 4y = 200 ...... Ecuación 1

Hoy

Hoy compré 2 cajas más de plaquetas y otras 2 de tejas por 130 €.

2x + 2y = 130 ..... Ecuación 2

Resolvemos usando el método de Eliminación

2x + 4y = 200 ...... Ecuación 1

2x + 2y = 130 ..... Ecuación 2

Restar la ecuación 2 de 1

2 años = 70

y = 70/2

y = 35 €

Resolviendo para x

2x + 4y = 200 ...... Ecuación 1.

2x + 4 × 35 = 200

2x + 140 = 200

2x = 200 - 140

2x = 60

x = 60/2

x = 30 €

el costo de

Caja de plaquetas = x = 30 €

Caja de azulejos = y = 35 €

Please please help!!! Giving brainiest

Answers

Answer:

8.8 ounces

Step-by-step explanation:

3.96 ÷ 0.45 = 8.8

she bought 8.8 ounces of ground coffee


someone help with the first one

Answers

Answer:

45

Step-by-step explanation: 180- 135

Answer:

<L = 45

<N = 135

Step-by-step explanation:

<L + 135 = 180

<L = 180 - 135

<L = 45

<N = 135 because of vertical angles

How much would $125 invested at 8% interest compounded continuously be
worth after 16 years? Round your answer to the nearest cent.
A(t)= P*e^rt

Answers

Answer:

449.58

Step-by-step explanation:

125e^(0.08)(16)

use desmos scientific caclulator

The plane has traveled 105 miles which is 45%of the distance it needs to go. How many miles is the total distance of the flight?

Answers

Answer: 162.75 miles

Step-by-step explanation: 100%-45%=55%

55%=.55

105 times .55= 57.75

105+57.75= 162.75

sorry but I'm not sure if its right because I haven't does one of these in a while

1) What is the value of x + 2 in this equation?
7(x + 2) = 77
2 + 2 =

Answers

7(x+2)=77
7x+14=77
-14=-14
7x=63
_. _
7. 7
X=9

2. Let u = <4, 8>, v = <-2, 6>. Find u + v. (1 point)

Answers

Answer:

u+v = (4,8)+(-2,6)

=(4-2, 8+6)

=(2, 14)...This is the required answer.

HELP ME WITH THIS PLEASE :)

Answers

Answer:

1) F

2) C

3) A

4) H

Step-by-step explanation:

1)

P = a + b + c + d

P = 7x + 8 + 7x + 8 + 9x + 4 + 12x - 2

P = 35x + 18

2)

P = 4a

P = 4(4x - 8)

P = 16x - 32

3)

P = 5a

P = 5(2x - 4)

P = 10x - 20

4)

P = 4a

P = 4(7x + 2)

P = 28x + 8

How many different 2-digit numbers can be formed from the digits 4, 6, and 8?

Answers

Answer:

12 two

24 and 42 represent one combination, but 2 permutations. Thus, the number of two-digit numbers that can be made with the digits 2, 4, 6, and 8 is: Therefore, 12 two-digit numbers can be made with the digits 2, 4, 6, and 8.

Step-by-step explanation:

please mark this answer as brainliest, leave a 5-start rating, and give a thanks

The number of 2-digit numbers can be formed from the digits 4, 6, and 8 is 18.

What is the Permutations?

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

The given digits are 4, 6 and 8.

We know that, P(n, r)= n!/(n-r)!

Here, n=3 and r=2

Now, 3!/(3-2)!

= 3×2

= 6

Using C(n, r)= n!/r!(n-r)!

Now, 3!/2!(3-2)!

= 3

So, 6×3

= 18

Therefore, the number of 2-digit numbers can be formed from the digits 4, 6, and 8 is 18.

To learn more about the permutation visit:

https://brainly.com/question/3867157.

#SPJ6

Please help with these 2 range questions ❤

Answers

Answer:

10) 27

15) 18

Step-by-step explanation:

10)

Range = Max value - Min value

18 = x - 9

x = 27

15)

Range = Max value - Min value

32 = 50 - x

-x = 32 - 50

-x = -18

x = 18

Answer:

27 and 18

Step-by-step explanation:

The range is the difference between the largest and smallest numbers

(10)

Given range = 18 and smallest number is 9 then

largest number = 9 + 18 = 27

(15)

Given range = 32 and largest number is 50 , then

smallest number = 50 - 32 = 18

Celular limpio es frase o oracion

Answers

Answer:'

Frase

Step-by-step explanation:

Frase

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