Find the following for the nth term of the following geometric sequence, as an expression of n:

3, 15, 75, 375

Answers

Answer 1

Answer:

[tex]15^{n-1}[/tex]

Step-by-step explanation:

First , Let's find the common ratio of this sequence.

[tex]\frac{15}{3}=5\\\frac{75}{15} = 5\\\frac{375}{75} = 5[/tex]

SO,

r = 5

Now let's use this formula to find the n th term

[tex]T_n = ar^{n-1}[/tex]

Here,

a = first term

r = common ratio

Let's find,

[tex]T_n = 3*5^{n-1}[/tex]

[tex]T_n =15^{n-1}[/tex]

Therefore,

the n th term is,

[tex]15^{n-1}[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer 2

Answer:

[tex]a_{n}[/tex] = 3[tex](5)^{n-1}[/tex]

Step-by-step explanation:

There is a common ratio between consecutive terms , that is

15 ÷ 3 = 75 ÷ 15 = 375 ÷ 75 = 5

This indicates the sequence is geometric with nth term

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 3 and r = 5 , then

[tex]a_{n}[/tex] = 3 [tex](5)^{n-1}[/tex]


Related Questions

HELP!!! IM CONFUSED

Answers

Answer:

2/3

Step-by-step explanation:

If we want to find the slope, the most easiest way to find the slope is to use 'Rise/Run'. Two points are given, lets use those points and find the slope.

=> We see that the rise is 2. So 2 will be our numerator,

=> We can also see that the run is 3. So 3 will be our denominator.

What do we get?

We get 2/3 as our slope. Therefore, B is our answer. Hoped I helped.

Your above-ground pool has sprung a leak, and you do not have a way to fix it. At 12 noon, the water in the pool is 5 feet deep (in other words, the water level is 5 feet above the ground). You are not sure how quickly the pool level is falling, so you check again after 40 minutes and see that the height of the water level is now feet. You notice that there is a relationship between the time that has passed to the height of the water level in the pool.

Answers

Answer:

Step-by-step explanation:

.Learning Task 2: Get the quotient of each item up to the nearest ten thousandths place. Then, round the decimals to their nearest thousandths. Number 1 is done for you.

1.45÷8= 5.6250 -5.625------- example

4.93÷9 = _____ - ______

2. 77÷9 = _____ - ______

5.88 ÷7= _____ - ______

3.81÷7= _____ - ______

6.55÷8=_____ - ______​

sorry if the numbers is a bit confusing

Answers

The responses for the quotient given to the nearest thousandths are

presented in the order of the of the questions as follows;

[tex]Question \ 4) \ \displaystyle \underline{\frac{93}{9} = 10.3333 \approx 10.333}}[/tex]

[tex]Question \ 2) \ \displaystyle \underline{\frac{77}{9} = 8.5555 \approx 8.556}[/tex]

[tex]Question \ 5) \ \displaystyle \underline{\frac{88}{7} = 12.4285 \approx 12.429}[/tex]

[tex]Question \ 3) \ \displaystyle \underline{\frac{81}{7} = 11.5714\approx 11.571}[/tex]

[tex]Question \ 6) \ \displaystyle \underline{\frac{55}{8} = 6.8750\approx 6.875}[/tex]

Reasons:

4. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{93}{9}}= \frac{90 + 3}{9} = 10 + \frac{1}{3} = 10.\overline 3[/tex]

Given that we have;

[tex]\displaystyle \frac{1}{3} = 0.\frac{10}{3} =0.3 \frac{10}{3} = 0.3333[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{93}{9} = 10.3333 \approx 10.333}[/tex]

2. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{77}{9}} = \frac{72 + 5}{9} = 8 + \frac{5}{9} = 8. \frac{50}{9} = 8.5\frac{50}{9} = 8.55\frac{50}{9} = 8.555\frac{50}{9} = 8.5555[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{77}{9} = 8.5555 \approx 8.556}[/tex]

5. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{88}{7}} = \frac{85 + 3}{7} = 12 + \frac{3}{7} = 12. \frac{30}{7} = 12.4\frac{20}{7} = 12.42\frac{60}{7} = 12.428\frac{40}{7} = 12.4285\frac{5}{7}[/tex]

[tex]\displaystyle \underline{\frac{88}{7} = 12.4285 \approx 12.429}[/tex]

3. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{81}{7}} = \frac{77 + 4}{7} = 11 + \frac{4}{7} = 11. \frac{40}{7} = 11.5\frac{5}{7} = 11.57\frac{10}{7} = 11.571\frac{30}{7} = 11.5714\frac{20}{7}[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{81}{7} = 11.5714\approx 11.571}[/tex]

6. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{55}{8}} = \frac{48 + 7}{8} = 6 + \frac{7}{8} = 6. \frac{70}{8} = 6.8\frac{60}{8} = 6.87\frac{40}{8} = 6.875\frac{0}{8} =6.8750[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{55}{8} = 6.8750\approx 6.875}[/tex]

Learn more here:

https://brainly.com/question/17913153

please help me with this math problem

Answers

Step-by-step explanation:

the group of x friends is SPLITTING the cost of $50. Therefore to find the amount each person pays after the split, you will divide 50 by the amount fo friends (x). Each person is also paying an extra $5 for dessert. Therefore, you will be adding that 5 to everyone's total after splitting.

So the equation you will get is

[tex]a(x) = \frac{50}{x} + 5[/tex]

Answer:

A(x)= (50/x)+5

Step-by-step explanation:

50 bucks divided by the number of people in the group which is X and each must also pay 5 bucks for dessert.

Simplify.

x2+2x−3/
x−4/
2x2+5x−3/
x^2−16



x2−x−12/2x−3

x2−5x−4/2x−1

x2+3x−4/2x−1

x2+x−12/2x−3

Answers

Answer:

x^2 + 7x- 3/x - 3/x^2 -16

Step-by-step explanation:

Key:  ( ^ ) means exponent

= x^2 + 2x- 3/x -2x^2 + 5x- 3/x^2 -16

= x^2 - 2x^2 + 2x+5x - 3/x- 3/x^2 -16

= x^2 - 2x^2 = -x^2

=  -x^2 + 2x + 5x- 3/x- 3/x^2-16

As you see you add 2x and the 5x and got 7x

= Answer : x^2 + 7x- 3/x - 3/x^2 -16

Answer:

I think the answer is x^2+3x-4/2x-1

YES I WILL BE GIVING A BRANLIST
Which function has the greater rate of change? What is that value?

Answers

Answer:

To find the rate of change you use the formula, Y2-Y1/X2-X1.

Function A:

You can substitute in any two points. The points I will use are (0,0) and (1,1).

1-0/1-0

1/1

1

The rate of change for Function A is 1.

Function B:

The points I will use are (2,1) and (4,2).

2-1/4-2

1/2

The rate of change for Function B is 1/2.

Since 1 is larger than 1/2, Function A has a larger rate of change. The value is 1.

Hope this helps! :)

please help with statistic 20

Answers

Part A

p = 0.32 = probability of someone voting by internet

n = 13 = sample size

x = 10 = number of people who voted by internet

Apply the binomial probability formula.

[tex]P(x) = (_n C _x)*(p)^{x}*(1-p)^{n-x}\\\\P(10) = (_{13} C _{10})*(0.32)^{10}*(1-0.32)^{13-10}\\\\P(10) = (286)*(0.32)^{10}*(0.68)^{3}\\\\P(10) \approx 0.0010124942242\\\\P(10) \approx \textbf{0.00101}\\\\[/tex]

Note: the [tex]_n C_x[/tex] refers to the combination formula.

Answer:   0.00101

=============================================================

Part B

We could apply the binomial theorem for the following values of x: {10,11,12,13}. Then would add up the results.

However, such a task is fairly tedious and it's more efficient to use computer software (or a graphing calculator). Also, there's the element of limited time that you'll need to consider. I showed the steps for part A above because your teacher may have wanted you to list them. Usually it's better to rely on software for that task as well. At the very least, it's useful to have software to check your answer.

Whichever method you use, you should find the following:

P(10) = 0.00101P(11) = 0.00013P(12) = 0.00001P(13) = 0

The last value isn't exactly 0, but it's so small that it's effectively zero. This is because we only have 5 decimal places to work with.

Add up those four values to get:

[tex]P(x \ge 10) = P(10)+P(11)+P(12)+P(13)\\\\P(x \ge 10) \approx 0.00101+0.00013+0.00001+0\\\\P(x \ge 10) \approx 0.00115\\\\[/tex]

A faster shortcut is to use your calculator's binomCDF function.

This result of 0.00115 is fairly small. The usual distinction we make between whether a probability is small or not is to set up some kind of threshold. This threshold is known as the significance level. By default, it's set to 0.05 unless your teacher specifies otherwise. Another common significance level is 0.01, but it's usually mentioned.

Since 0.00115 is smaller than 0.05, and even 0.01, we consider the probability of getting 10 or more internet voters to be a significant event. It's fairly unusual to get 10 or more people voting by internet in this sample of n = 13 people.

Answer: Choice A) Yes, because the probability of 10 or more is 0.00115, which is low.

=============================================================

Part C

Like with part B, we could find the binomial probability values for x = {1,2,3,...,11,12,13}. We could add up the values like I did, or use the binomCDF function which is faster.

Another approach is to use the complement of the event "at least 1". If x is some number in the set {0,1,2,..,12,13}, then either [tex]x = 0[/tex] or [tex]x \ge 1[/tex]

From this, we can say

[tex]P(x=0) + P(x \ge 1) = 1\\\\P(x \ge 1) = 1-P(x=0)\\\\P(x \ge 1) \approx 1-0.00665\\\\P(x \ge 1) \approx 0.99335\\\\[/tex]

This then rounds to 0.993

Answer:  0.993

What is the next term in the sequence 58, 47, 36, 25,. ? –58 –8 14 69.

Answers

Answer:

14

Step-by-step explanation:

58, 47, 36, 25,. ?

Each term is 11 less than the preceding term

the term after 25 will be

25 - 11 = 14

plz help i give brainliest and points

Answers

Answer:

Step-by-step explanation:

To find this, lets make a equation.

We have the expression 8b - 27, lets set this equal to -11 and solve:

8b -27 = -11

Now lets solve.

Lets add 27 to both sides to get 8b alone:

8b = 16

Now lets divide by 8:

b = 2

So our answer is 2.

Hope this helps!

I believe it’s 2, I’m not completlyyyyyy sure

Los asistentes, hoy, a la reunión semanal de un club social se pueden agrupar por parejas para bailar, por tríos para hacer manualidades, y de 4 en 4 para jugar bingo. En ninguno de esos casos queda nadie sin grupo. ¿Cuántas personas son si casi llegan a 25?

Answers

En la reunión semanal había 24 personas.

Los asistentes, hoy, a la reunión semanal de un club social se pueden agrupar por parejas para bailar, por tríos para hacer manualidades, y de 4 en 4 para jugar bingo, y en ninguno de esos casos queda nadie sin grupo, para determinar cuántas personas son si casi llegan a 25 se debe realizar el siguiente cálculo, obteniendo el múltiplo común entre estos números:

2 - 4 - 6 - 8 - 10 - 12 - 14 - 16 - 18 - 20 - 22 - 243 - 6 - 9 - 12 - 15 - 18 - 21 - 244 - 8 - 12 - 16 - 20 - 24

Por lo tanto, en la reunión semanal había 24 personas.

Aprende más en https://brainly.com/question/3113448

what is the correct Answer?!

Answers

Answer:

B

Step-by-step explanation:

2⁶

2⁶

then add the ⁶+³+⁶+³ =18

2¹⁸

hi please help me with part b and can you see if i did a correctly pls?

Answers

a is right its 58

and in my opinion i think b would be 58*5=290 cents, since nickel is worth 5 cents.

but gotta check other people's answers

given g(x)=-2x+1 solve for x when g (x)=5

Answers

Answer:

x = -2

Step-by-step explanation:

g(x) = 5

-2x + 1 = 5

-2x  = 5 - 1

-2x = 4

x = 4/-2

x = -2

>> Answer

_________

[tex]\:[/tex]

g(x) = 5

5 = -2x + 1

5 - 1 = -2x

4 = -2x

x = -2

If A(2, 3) and B(-4, -6), find AB.--

Answers

[tex] \huge \bf༆ Answer ༄[/tex]

The distance between points can be solved using Distance formula (similar to Pythagoras theorem)

[tex] \boxed { \sf D = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1) {}^{2} } }}[/tex]

Put the values : -

[tex] \sf D = \sqrt{ (2 - ( - 4)) {}^{2} + (3 - ( - 6)) {}^{2} } [/tex]

[tex] \sf \: D = \sqrt{ {(6)}^{2} + (9) {}^{2} } [/tex]

[tex] \sf D = \sqrt{36 + 81} [/tex]

[tex] \sf D = \sqrt{117} [/tex]

[tex] \sf D = 3 \sqrt{13} [/tex]

Distance between the points = 3√13 units

[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]

Answer:

If you are trying to find the line, simply use a graph.

Step-by-step explanation:

HELP!! Highschool math

Answers

Answer:

What does this mean?

Step-by-step explanation:

So you need to divide the m by 234 and after you got your answer you would need to times it by 156

Jessica and her brother collects stamps. When Jessica gives her brother 1% of her stamps, she has 2,475 stamps left. Calculate how many stamps Jessica had originally.

Answers

Answer:

2500

Step-by-step explanation:

2475 stamps is 99% of her original number of stamps.

SO,

[tex]2475 \div 99\% = 2500[/tex]

She originally had 2500 stamps

ACCURATE ANSWER=BRAINLIST
The first four terms of a sequence are shown.

7, 25, 43, 61, ...
Which of the following expressions can be used to find the nth term of the sequence?

Question 3 options:

7+18n

18+7n

18+7(n−1)

7+18(n−1)

Answers

Answer:

7+18n

might be the answer sorry if I am wrong

It’ be 7 + 18(n-1)

I plugged in the fourth term for n, and only that expression gave the correct answer of 61

Finding slope from tables and

Answers

Answer:

m=-5/2 b=2

Step-by-step explanation:

It goes over 2 times ever time it goes down 5 times. and when the y is 0 the x is 2

Mason gave the waiter a $14.58 tip, which was 15 percent of the dinner bill. What was the amount of the dinner bill before he added the tip?
$9.72
$21.87
$97.20
$218.70

Answers

Answer:

$97.20

Step-by-step explanation:

97.20 x 0.15 = 14.58

Multiply the total by 15 percent, giving you the $14.58 tip, proving it to be correct.



Sully built a shelf 8 5/8 inches wide for his DVD collection. If each DVD is 3/8 inches
wide, how many can he fit on the new shelf?

Answers

Answer:

23

Step-by-step explanation:

8 5/8 = 69/8

Each DVD is 3/8 inches

Ignore the denominators

We have 69 and 3

69 is 23 times bigger than 3, so 23 DVD's can fit

what is the solution to the system of equations​

Answers

Here the answer hope this help

A) (2x-10)(3x+1)
B) (3x+2)(2x-5)
C) (2x+5)(3×+1)
D) (2x+1)(3×+5)
E) None of the above. The quadratic f(x) = 6x] + 11X - 10
would have which of the following
factors?

Answers

Answer:

B

Step-by-step explanation:

(3x+2)(2x-5)

Brainliest?

Guided Practice

Type your answer and then click or tap Done.
Use the ^ symbol (Shift+6 on the keyboard) to signify an exponent. For example, for 2 to the third power, enter 2^3.

Identify the quadratic term in the function.

f(x)=2x^2−3x+5

Answers

Answer:

2x^2

Step-by-step explanation:

Q:

identify the quadratic term in the function f(x)=2x^2-3x+5

A:

The quadratic term is 2x^2.

Answer:

2x2-3x-5=0

Step-by-step explanation:

(2x2 -  3x) -  5  = 0

Answer:

The quadratic term in the function is  

Step-by-step explanation:

Given : Function  

To find : Identify the quadratic term in the function ?

Solution :

The quadratic  form of the function is  

Where,  is quadratic term.

On comparing with given function,  

is the quadratic term.

Therefore, the quadratic term in the function is

Em uma avaliação que vale até 5 pontos, João tirou 4,2 pontos. Quanto João teria tirado caso a prova valesse 10 pontos?

Answers

Answer:

8.4 pontos

Step-by-step explanation:

4.2/5

multiplique o numerador e o denominador por 2

8.4/10

3x-8=3(1x-3)-2

whats the answer to that problem

Answers

Answer:

-3

Step-by-step explanation:

......................

Which function has the graph shown below? *

a. f(x) = x² - 4
b. f(x) = x² + 4
c. f(x) = (x + 4)²
d. f(x) = (x - 4)² opps dont forget to change the sign​

Answers

Answer:

C

Step-by-step explanation:

yeah-ya......... right?

A store owner has 65.5 pounds of candy. If he splits the candy equally into 5 boxes, how many pounds of candy will each box contain?

Answers

Answer: Each box of candy would contain 13.1 pounds of candy.

Step-by-step explanation:

Divide 65.5 by 5. Hope this helps!

HELP DUE IN 1 MINUTE 5x^3 + 20x^2-160x

Answers

5x(x-4)(x+8) should be ur answer

Write the equation of the following parabolae in their canonical form and hence find their vertices, foci and directrix.
1.
[tex] {y}^{2} - 6y - 2x + 19 = 0[/tex]
2.
[tex] {x}^{2} + 4x + 4y + 16 = 0[/tex]

Answers

#1

Given:

y² - 6y - 2x + 19 = 0

This is a horizontal parabola.

Canonical form of horizontal parabola is:

4a(x - h) = (y - k)², where (h, k) is vertex

Focus is:

F(h + a, k)

Directrix is:

x = h - a

Convert the equation:

y² - 6y - 2x + 19 = 0y² - 6y  + 9 - 2x + 10 = 0(y - 3)² = 2x - 10(y - 3)² = 4(1/2)(x - 5)

We got:

h = 5, k = 3, a = 1/2

Focus is:

F(5 + 1/2, 3) = F(5.5, 3)

Directrix is:

x = 5 - 1/2 = 4.5#2

Given:

x² +4x + 4y + 16 = 0

This is a vertical parabola.

Canonical form of vertical parabola is:

4a(y - k) = (x - h)², where (h, k) is vertex

Focus is:

(h, k + a)

Directrix is:

y = k - a

Convert the equation:

x² + 4x + 4y + 16 = 0x² +4x + 4 + 4y + 12 = 0(x + 2)² = -4y - 12(x + 2)² = 4(-1) (y + 3)

We got:

h = - 2, k = -3, a = - 1

Focus is:

F(-2, -3 - 1) = F(-2, - 4)

Directrix is:

y = -3 - (-1) = - 2

What number is furthest from 0 on a number line? 16 or 18?

Answers

18. _______________________________________
Other Questions
1. Explain the relationship between the Speedy Trial Act of 1974 and the Sixth Amendment.2. Do you think the Criminal Justice System does a good job at protecting the defendant's Sixth Amendment Right? Why or why not? Give evidence to support your answer. do you like ice cream or cake better explain 13 cm5 cm7 cm12 cmFind the surface area. Find the slope of a line parallel to each given line.a -7x = 3y + 12 What is the function of a claim in an argument ? Two common ____________ are the balance sheet and the income statementA. financialB. financial statementsC. reportD. statements please help quickly solve this What is the length of each side of this equilateral triangle? A) 42B) 30C) 15D) 12 What is a short-constructed response? What arethe necessary components of a short-constructed response? If 4 gallons of milk cost $16.24, how much would 7 gallon of milk cost Scientists unearth one of the oldest known dinosaurs. Millions of years ago, a bloodthirsty dinosaur roamed Earth. The rough reptile terrorized its prey, viciously ripping apart animals with its sharp claws and knife-like teeth. Who was this fierce hunter? No, not Tyrannosaurus rex. It was Eodromaeus-a dinosaur the size of a dog! Scientists recently introduced the teeny meanie, whichthey discovered in Argentina. That is a country in South America. Experts say Eodromaeus (ee-oh- DROH-mee-uhss) is one of the oldest dinosaurs ever discovered. It lived during the Triassic Period about 230 million years ago. The dinosaur's name means "dawn runner." The pint-sized predator was four feet long from nose to tail and weighed less than fifteen pounds. Though Eodromaeus was small, it may hold big clues about the world's first dinosaurs."We're looking at a snapshot of early dinosaur life," says Paul Sereno. He is a paleontologist who helped find the reptile.A Meaty History Eodromaeus has a history that scientists can really sink their teeth into. The dinosaur was one of the very first theropods. A theropod was a meat-eating dino that walked on two legs. The great-granddaddy of T. rex shared some key features with later carnivores, or meat eaters. The reptile had sharp, narrow teeth. "They have small, steak knife-like [edges] so that when they are jabbed into flesh, they open a wound," Sereno explained to WR News. Eodromaeusmost likely chowed down on small dinosaurs and the young of other reptiles. Also, like later meat eaters, the dinosaur had hands that were perfect for grabbing its dinner. "The bones behind the claws are very long, so it can get the claw around something," Sereno explains.In addition, the end of the dino's tail was stiff to let Eodromaeus keep its balance while running.The Big Reveal Eodromaeus is helping scientists learn about other early dinosaurs. The reptile shared its turf with a similar-looking dinosaur called Eoraptor (ee-oh-RAP-tor). For years, experts suspected, or thought, that Eoraptor ate meat. But after comparing Eoraptor's and Eodromaeus's features, they determined that Eoraptor was an herbivore, or plant eater. Despite the dinos' different diets, they had a lot in common, including their size, experts say. "I think if they [ran] by, you might not even know the difference except that one might want to rip your arm off and the other one might ... hide in a bush," Sereno says. The fact that the dinosaurs shared so many features could mean that they are also very similar to the world's first dinosaur, Sereno says. Experts believe that dino roamed Earth ten million years earlier than Eoraptor and Eodromaeus did. That may seem like a long time, experts say, but it is relatively short compared with the 183 million years that dinosaurs existed.Digging Deeper Sereno and his team found both Eodromaeus and Eoraptor in northern Argentina. They believe the country may hold even more fossils-including the remains of the very first dinosaur. "We're going to go back," Sereno says. He's pretty sure some fossils will turn up. "They always come out to say hi when we come!"Profile of a Predator Small animals, beware! Eodromaeus's skeleton shows certain features that are common in all meat-eating dinosaurs, including T. rex. WHAT IS THIS ABOUT Is 666 = 37 positive or negative? 7.0g divided by 5.6g/cm cubed The big worry at the chapter's end isQuestion 5 options:dividing the treasureSmaug's locationreplacing the ponies Jumbled Words: Arrange the following words. (KITCHEN WEARS/TOOLS/EQUIPMENT)1. IBCENTAN - 2. WDRRAE - 3. OTLEW - 4. ISETUS - 5. NIKS - 6. BLETA KPANNI - 7. LEPAT - 8. SAGLS - 9. RFKO - 10. NOSOP -This is URGENT! 5 MIN. LEFTY'all i need this to be doneee!! Don't answer this quest if you don't know what's the answer.. Thanks!! Helpful answer/w explanation = Brainliest Answer Unhelpful answer/ Nonsense = Report (Delete) What is the equation of the line in slope-intercept form?Write your answer using integers, proper fractions, and improper fractions in simplest form. Diedres sister works as a lifeguard. Last summer she earned $14 per hour. She earned a total of $5,180 workingas a lifeguard last summer. How many hours did Diedres sister work as a lifeguard last summer? is 10/110 an irrational or rational number The hypotenuse of a certain number is 5 units and one leg is 3 units long. Find the area of the triangle name and briefly summarize the clause of the u.s. constitution that grants the government the power to regulate business. provide an example of government regulation of business.