Write an explicit formula for an,the Nth term of the sequence 4,12,36

Answers

Answer 1

Answer:

[tex]3^{n}+3^{n-1}[/tex]

Step-by-step explanation:

Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be [tex]x^n + yn[/tex]

Because the sequence multiplies by 3 each time, The base number in that equation would be [tex]3^n +yn[/tex].

So [tex]3^n[/tex] of the equation would be:
[tex]3, 9, 27[/tex].

Compare the 2 equations:
4, 12, 36

3, 9 ,27

The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: [tex]3^{n-1}[/tex].

Combine these 2 equations together and you get:

[tex]3^{n}+3^{n-1}[/tex].


Related Questions

grace likes jeffery what will she do ?

Answers

Answer:

2,964

Step-by-step explanation:

52 x 57 = 2,964

sophie leaves school and travels east at an average speed of 40km/h, jenny leaves school one hour later and travels west at an average speed of 50km/h, determine how many hours after jenny leaves school they will be "400km" apart

Answers

Considering the speeds given, it is expected Sophie and Jenny are 400 km apart after a total of 5 hours.

How will their position change over time?

Jenny:

1 hour later:  40 km east2 hours later: 80 km east3 hours later: 120 km east4 hours later: 160 km east5 hours later: 200 km east

Sophie:

1 hours later: 0 km2 hours later: 50 km west3 hours later: 100 km west4 hours later: 150 km west5 hours later: 200 km west

When wil they be 400 km apart?

It is expected 5 hours later they are 400km apart because at this time each of them will be 200km away from school.

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What is the length of line segment b c? round to the nearest tenth. 14.3 in. 20.5 in. 21.3 in. 22.6 in.

Answers

The given figure is a triangle with 3 sides and angles. The length of BC as shown in the diagram is 20.5in

SOH CAH TOA identity

The given figure is a triangle with 3 sides and angles. In order to determine the length of BC, we will use the expression given:

cos 35 = a/25

where a = BC

cos 35 = BC/25
BC = 25cos 35
BC = 20.5in

Hence the length of BC as shown in the diagram is 20.5in

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The area of a circle is 60.12cm find the length of the radius rounded to 2 dp.

Answers

Answer:

Before you write the answer to your question, make sure the question is asking for the actual value of pi or 3.14.

If the question was asking for the question to be completed with the ACTUAL VALUE of pi, then your answer is ----> 4.37

If the question was asking for the question to be completed with the rounded of pi (3.14), then your answer is ----> 4.38

It's a subtle difference, but remember, there is no such thing as close in math, it's either right or wrong.

Step-by-step explanation:

Given: Circle's Area, 60.12

As the value of pi was not directly stated, I will divide the answer into 2 portions, portion one with the answer with the actual infinite value of pi, and one where I will describe how to do it with 3.14 as pi.

Explanation with 3.14:

First thing first, know the formula for calculating the area of a circle:

[tex]A = \pi r^2[/tex]

[tex]A[/tex] stands for Area, and [tex]r[/tex] stands for Radius

Now, plug in the given values:

[tex]60.12 = \pi r^2[/tex]

Next, replace 3.14 for pi:

[tex]60.12 = (3.14)r^2[/tex]

Then, divide both sides by 3.14 ,which gives us:

[tex]19.15 = r^2[/tex]

Please note: 19.15 is rounded

Anyway, to isolate [tex]r[/tex], we take the square root of both sides:

[tex]\sqrt{19.15} = \sqrt{x^2}[/tex]

The square root and square on the right side of the equation cancel out, and we are left with:

[tex]4.38 = r[/tex]

Please note that 4.38 was rounded

What is the image point df (-2, -3) after a translation right 2 units and up 4 units?

Answers

Answer:

(0, 1)

Step-by-step explanation:

right 2 units: add 2 to x

up 4 units: add 4 to y

Answer: (0, 1)

can anyone tell me what angle Y is?

Answers

Answer:

Step-by-step explanation:

93 + y = 180

y = 180 - 93

y =87 Degrees

Answer:

87°

Explanation: The angles y and 93° are supplementary angles.

Therefore, subtract 93° from 180°, and voila! You got the answer.

David bought a computer that was 20%
off the regular price of 1,080.if an 8%
sales tax was added to the cost of the
computer what was total price david
paid for it

Answers

Answer:

The total price David paid for the computer is $933.12

Step-by-step explanation:

The cost of the computer will be $1,080 with 20% off and 8% sales tax.


20% of 1080 is 1080(0.20)=216 this means 216 is 20% of 1080, so with the discount the price will be 1080-216=$864

Now we have to find 8% of 864.

864(0.08)=$69.12

So the total price will be 864+69.12= $933.12

this is an escape room i can't escape

Answers

Answer:

The area of the rectangle is 180 units

Step-by-step explanation:

6 + 2 + 2 = 10

But the areas of each sectioned off shape are

Big rectangle = 180

Small rectangle = 48

2 by 8 triangles = each 8

3 by 8 triangles = each 12

Altogether, it's 268

Answer:

268 square yards

Step-by-step explanation:

small L rectangle   8 x 6 =48

two L triangles   2    * 1/2 * 2 * 8 = 16

Large rectangle 18 x 10 = 180

two R triangles    2    * 1/2 3 x 8 =24    Total = 268 yds^2


find x and y…………….????????

Answers

Answer:

[tex]let \: \alpha \: be \: the \: 45 \\ \tan( \alpha ) = \frac{p}{b} \\ \tan(45) = \frac{x}{3 \sqrt{2} } \\ 1 = \frac{x}{3 \sqrt{2} } \\ x = 3 \sqrt{2} \\ by \: using \: pythagoras \: therom \\ {y}^{2} = {3 \sqrt{2} }^{2} + {3 \sqrt{2} }^{2} \\ {y}^{2} = 18 + 18 \\ y = \sqrt{36} \\ y = 6[/tex]

Step-by-step explanation:

hope this will help you

6
7
2
5
The usual price of a TV set was $400. During Memorial Day weekend, the price was marked down to
$335. What was the percent decrease in the price of the TV set?
сл

Answers

Answer:

The answer is 65% is the percent decrease

what can Tiffany conclude from the data above?​

Answers

A person who has only a high school diploma, they are most likely to have an income of less than $40,000.

What is probability?

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

The probability of a high school diploma person having less than $40,000 income will be

P(HSD) = 51/78

P(HSD) = 0.6538

The probability of a Bachelor's degree person having less than $40,000 income will be

P(BD) = 24/78

P(BD) = 0.3077

The probability of a master's degree person having less than $40,000 income will be

P(MD) = 3/78

P(MD) = 0.0385

A person who has only a high school diploma, they are most likely to have an income of less than $40,000.

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help it’s due in an hour and I’m stuck

Answers

Height for row A is 5x+5

Base for row B is 8x-3

Height for row C is 2x+y

Pls answer the follwing

Answers

Answer:

Step-by-step explanation:

4 (x + 2) =30

4x + 8 = 30

4x = 30 - 8

4x = 22

x = 22 : 4

x = 5.5

check

(5.5 + 2) * 4 = 30

the answer is good

Answer:

the cost of each sandwich is 5.5

Step-by-step explanation:

we have,

4(x+2) = 30

we know a(b+c) = ab+ac

so, when we open the bracket we get,

4(x+2) = 4x+4*2 which is equal to 4x+8

so, 4x+8 = 30

=>   4x = 30 - 8         [transposing method]

=>   4x = 22

=>   x = 22/4

=>   x = 5.5

hope this helps

Write 0.030 in scientific notation

Please help :)

Answers

Answer: 3x10^-2

Explanation: Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10.
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

The volume of a cylinder is 4πx3 cubic units and its height is x units.


Which expression represents the radius of the cylinder, in units?

: 2x, 4x

Answers

Expression represents the radius of the cylinder, 2x units.

What is a cylinder?

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

Given that:

Volume of cylinder =[tex]4\pi x^{3}[/tex]

we know that, Volume of cylinder = [tex]\pi r^{2} h[/tex]

[tex]4\pi x^{3}[/tex]= π * [tex]r^{2}[/tex] *h

[tex]4x^{3} = r^{2}*h[/tex]

[tex]4x^{3} = r^{2}*x[/tex]      [since, height=x]

[tex]4x^{2} = r^{2}[/tex]

r= 2x

Hence the radius of the cylinder is 2x units

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A pole 3.8 m high casts a shadow that measures 1.3 m. A nearby tree casts a shadow 7.8 m long. Find the height of the tree.​

Answers

Answer:

22.8 m

Step-by-step explanation:

the 2 situations are similar triangles

the ratio of corresponding sides are in proportion

let h be the height of the tree , then

[tex]\frac{h}{3.8}[/tex] = [tex]\frac{7.8}{1.3}[/tex] ( cross- multiply )

1.3h = 29.64 ( divide both sides by 1.3 )

h = 22.8 m

The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a moving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation.

Answers

Answer:

Hello!!!

In this specific case the constant of proportionality is s (speed).

Step-by-step explanation:

The constant of proportionality stay "constant" (as the name suggests) in a certain case.

meaning, the speed itself remains constant at any given distance or time.

You can use the constant of proportionality and either distance or time to find the missing varliable since it remains constant.

you can also switch up the formula:

d=st

t=d/s

s=d/t

i really hope this helps!!!!!

Can someone please answer my trigonometry problem? I've been trying to get answers all day for something so minimal.

Find each measurement indicated. Round your answers to the nearest tenth.

Answers

Answer:

  ∠B ≈ 30.0°

Step-by-step explanation:

The law of sines can be used to solve a triangle when two sides and an angle opposite one of them are given.

__

  sin(B)/b = sin(C)/c

  sin(B) = (b/c)sin(C) . . . . solve for sin(B)

  sin(B) = (14/28)sin(91°) ≈ 0.49992385

The angle is found using the inverse sine function:

  B = arcsin(0.49992384) ≈ 29.99496°

Rounded to tenths, the angle is ...

  m∠B ≈ 30.0°

_____

Additional comments

Many triangle solver apps and web sites are available if all you want is an answer.

When using your calculator, be sure the angle mode is set to "degrees."

The Law of Sines can also be used to solve a triangle when two angles and one side are known.

please answer this for me

Answers

Answer:

600 + 161 = 761

Step-by-step explanation:

599 + 162 = 600 + 161 = 761

X=-3
A. 64
B. 8
C. 4
D. 16

Answers

Answer:

The answer is A.

Step-by-step explanation:

I took the test

The measures of the angles of a triangle are shown in the figure below solve for X

Answers

Answer:

29 degrees

Step-by-step explanation:

The interior angles of all triangles equals 180. We know already that we have 101 and 50 degrees. If we add that, we get 151. To find x, we have to simply subtract 151 from 180. If we do this, we get 29. x=29.

Hope this helps!

Find the area of the rhombus

Answers

[tex]60cm^{2}[/tex]

Step-by-step explanation:

A=pq/2

shorter diagonal= 8cm

longer diagonal = 15cm

15*8 = 120

120/2 = 60

A = [tex]60cm^{2}[/tex]

A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?


I aded the graph

Answers

Answer:

D. 80

Step-by-step explanation:

The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.

200 × .375 = 75

75 rounded to the nearest tens value is 80

There are 7 seniors on the high school soccer team. Two of them will be
chosen to be co-captains. How many ways are there to choose the co-
captains?
Decide if this is a permutation or a combination, and then find the number of
ways to choose the co-captains.

Answers

The action to choose two among the seven seniors to be cocaptains is a combination and there are 21 different choices.

What is a the difference between permutation and Combination?

The major difference between permutation and Combination lies in the fact that the different ways of arranging a set of objects into a sequential order are termed as Permutation while one of the several ways of choosing items from a large set of objects, without considering an order is termed as Combination.

On this note, the action is a combination and the number of ways is; 7!/5!2! = 21.

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If Saul CANELO Alvarez has 8 belts how many belts would he have it 34 were taken away

Answers

Answer:

42

Step-by-step explanation:

I would guess that Saul had 42 belts before because 42-34 is 8

Divide and write the quotient as a decimal

Answers

Answer:

0.16666666666667.

Step-by-step explanation:

n the diagram, what is AC?

A.
6

B.
12.33

C.
10

D.
12

Answers

Answer:

since we are not given the value of AC we say that AC =6×10=60

Erin has four shirts (whites, blue, red, black) and two pairs of pants (black, blue). She randomly chooses a shirt and a pair of pants. what is the probability that they are the same color?

Answers

Answer:

25%

Step-by-step explanation:

Where can i revise for my end of year maths assessment

Answers

Answer:

Huh??

where on brainly

Step-by-step explanation:

Amanda measures the top of an 80 cm
desk to be 82.4 cm. Dwayne measures
the height of a 140 cm cabinet to be
a
137.2 cm. Which student has a greater
percent error?

Answers

Answer:

Amanda's percent of error: = .03 or 3% Dwyane's percent of error: = .02 = 2%

Looks like Amanda had the larger error.

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