Determine whether the sequence converges or diverges. If it converges, give the limit.


9, 27, 81, 243,

Answers

Answer 1

The sequence diverges because the value of the absolute common ratio r is greater than the 1.

What is convergent of a series?

A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.

We have series:

9, 27, 81, 243....

The above series is a geometric progression with common ratio r is 3

[tex]\rm r =\dfrac{27}{9}[/tex]

r = 3

We know the formula for a geometric sequence:

[tex]\rm S_n = 9(3)^n[/tex]

[tex]\rm S_n = 3^{n+2}[/tex]

A geometric series converges only if the absolute value of the common ratio:

r < 1  and

It diverges if the ratio ≥ 1

Here the value of r = 3 which is greater than the 1 so the sequence diverges.

Thus, the sequence diverges because the value of the absolute common ratio r is greater than the 1.

Learn more about the convergent of a series here:

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Related Questions

Evaluate a+4a+4a, plus, 4 when a=7a=7a, equals, 7

Answers

The answer is 64 if you meant to say a + 4a+4a+ 4

(But if not it’s 60)

Answer:

the answer is 11

Step-by-step explanation:


Find the inverse function of y=7x.

Answers

Answer:

f^−1(x)=x7

Step-by-step explanation:

To find the inverse , inerchange the variable and slove for Y

If f(1) = 1 and f(n) = 5f(n-1) + 4 then find the value of f(5).

Answers

Answer:

[tex]f(5)=1249[/tex]

Step-by-step explanation:

Given:

[tex]f(1)=1[/tex][tex]f(n) = 5f(n-1)+4[/tex]

[tex]\implies f(2) = 5f(1)+4=5(1)+4=9[/tex]

[tex]\implies f(3) = 5f(2)+4=5(9)+4=49[/tex]

[tex]\implies f(4) = 5f(3)+4=5(49)+4=249[/tex]

[tex]\implies f(5) = 5f(4)+4=5(249)+4=1249[/tex]

f(n)=5f(n-1)+4f(2)=5f1+4=5+4=9f(3)=5f2+4=45+4=49f(4)=5f3+4=245+4=249f(5)=5f_4+4=1245+4=1249

does anyone know the answer?

Answers

Pretty sure it’s 20cm
Have a nice day

Answer:

C

Hope This Helps! :)

For funcitons f(x)=2x+3 and g(x)=-3x-2, please find (f∘g)(-1)

Answers

Answer:

[tex]\displaystyle (f\circ g)(-1) = 5[/tex]

Step-by-step explanation:

We are given the two functions:
[tex]\displaystyle f(x) = 2x + 3\text{ and } g(x) = -3x - 2[/tex]

And we want to find:
[tex]\displaystyle (f\circ g)(-1)[/tex]

Recall that this is equivalent to:
[tex]\displaystyle (f\circ g)(-1) = f(g(-1))[/tex]

Hence, find g(-1):
[tex]\displaystyle \begin{aligned} g(x) & = -3x - 2\\ \\ g(-1) & = -3(-1) - 2\\ \\ & = (3) - 2 \\ \\ & = 1 \end{aligned}[/tex]

Substitute:
[tex]\displaystyle f(g(-1)) = f(1)[/tex]

Find f(1):

[tex]\displaystyle \begin{aligned} f(x) & = 2x+ 3 \\ \\ f(1) & = 2(1) + 3 \\ \\ & = 5\end{aligned}[/tex]

In conclusion:
[tex]\displaystyle (f\circ g)(-1) = 5[/tex]

it cost 60$ to for 4 apples how much would 60 apples cost

Answers

Answer:

$900

Step-by-step explanation:

60/4 = 15

60 x 15 = 900

Answer:

900

Step-by-step explanation:

900 it's not that hard 60/4 15x60

Which number is closest to
68?
9
64
8
34

Answers

Answer:

64

Step-by-step explanation:

In how many ways can she grab 3 Snickers, 2 Starbursts, and 2 Reese's?

Answers

(1) Basket (2) Hands (3) Cart. 3 ways i can think of

Hep quickly for the brainliest answer quickly please no time

Answers

It would be B.
The 6 and 9 look the same up side down and so do the HOH

Please help me - geometry

Answers

Answer:

v≈4.7

w≈1.6

Step-by-step explanation:

sin71º=v/5

v=5*sin71º≈4.7

cos71º=w/5

w=5*cos71º≈1.6

Huan works at a pizza restaurant in the morning he made 23 pizzas to sell at noon he had five pizzas left how many pizzas did he sell

Answers

Answer:

18. Huan sold 18 pizza's. 23 - 5 = 18.

You can also start at 23, and count down to 5.

Step-by-step explanation:

what are the steps to solving 7(x+2)=91

X=11

Answers

Answer:

Below.

Step-by-step explanation:

7(x + 2) = 91

Distribute the 7 over the parentheses:

7x + 14 = 91

Subtract 14 from both sides of the equation:

7x = 91 - 14

7x = 77

x = 77/7 = 11.

Answer:

X=11

Step-by-step explanation:

[tex]7\left(x+2\right)=91[/tex]

Divide both sides by 7:

[tex]\frac{7\left(x+2\right)}{7}=\frac{91}{7}[/tex]

Simplify:

[tex]x+2=13[/tex]

Subtract 2 from both sides:

[tex]x+2-2=13-2[/tex]

Simplify:

X=11

Which table represents a function?


X y
-4 6
0 8
4 12


X y
-4 3
-2 6
-2 9


X y
-3 7
-1 9
-3 -7


X y
1 2
1 6
2 10

Answers

Answer:

-2x+4>18.

Step-by-step explanation:

Solve and graph a one variable inequality. Solve the inequality and graph the solution on a number line.

Answer 12 please thank you

Answers

Answer: 30%

Step-by-step explanation:

because my friend said so? <3

hope this helps!

Why is this a right triangle? A) Two angles are acute. B) One angle measures exactly 90°. C) All three angles are less than 90°. D) All three sides are of equal length.

Answers

Answer:

B)

Step-by-step explanation:

The main feature in a right triangle is that it has a right angle (90°)

Hope this helps

If a1 = 7 and an = an-1 + 4 then find the value of a4.

Answers

Answer:

[tex]a_4=19[/tex]

Step-by-step explanation:

Given:

[tex]a_1=7[/tex][tex]a_n=a_{n-1}+4[/tex]

[tex]\implies a_2=a_{1}+4=7+4=11[/tex]

[tex]\implies a_3=a_{2}+4=11+4=15[/tex]

[tex]\implies a_4=a_{3}+4=15+4=19[/tex]

Put values get answer

a_n=a_(n-1)+4a_4=a_3+4a_4=a_2+4+4a_4=a_1+4+4+4a_4=7+12a_4=19

What is the measure of WV
(Value of x is 19)

Answers

Do you really feel fly in true religion

Mr. Ramos's monthly mileage allowance for a company car is 750 miles. He drove 8 miles per day for 10 days, then went on a 3-day trip. The table shows the distance he drove on each day of the trip.

Trip Mileage

Day Miles Driven
Tuesday 156.1
Wednesday 240.8
Thursday 82.0
After the trip, how many miles remain in Mr. Ramos's monthly allowance? Record your answer in the box.

Answers

Answer:

558.9 miles total

Step-by-step explanation:

See attached spreadsheet.

Which of the following numbers are greater than or equal to 1.75?

Choose all answers

A) 1 4/11

B) 1.6
C) 7/4

Answers

Answer:

Only C

Step-by-step explanation:

1 4/11 is 1+4/11 and 4/11 is less than 1/2 so it has to be less than 1.5, which is less than 1.75

1.6 is less than 1.75 because 1.75-1.6 is 0.15 which is a positive number

4/7 is 1 3/4 which is 1.75

Answer:

a and c

Step-by-step explanation:

they are over 1

The cost, y, of red apples can be represented by the equation y = 2x, where x
is the number of pounds of red apples.
The graph shows the cost of green apples.
Which type of apple costs more per pound?
Cost of Green Apples
11
10
PLEASE HURRY I NEED IT IN 5 mins
Cost (5)
.
3
Weight (pounds)
A. Red apples
B. Red and green apples cost the same.
C. Green apples

Answers

Answer:

red apples

Step-by-step explanation:

1 lb of green apples is 1.5

1 lb of red apples is 2

My sister needs help again MATHHH

Answers

Answer:

31

Step-by-step explanation:

PEMDAS is Parentheses, Exponent, Multiplication, Addition, Subtraction

This is just the order you do the operations.

First, Parentheses.

Second, Exponents,

Third, Multiplication or Division

Last, Addition or Subtraction

So we have,

[6(20) + 3(15)] ÷ 5

We first look at Parentheses.

The first case is 6(20)

6(20) = 120

We have [120 + 3(15)]÷ 5

We solve 3(15) as its the next parentheses

3(15) = 45

We have [120 + 45] ÷ 5

Then we solve for [120 + 45] as it's in brackets.

[165] ÷ 5 = 31

The answer is 31.

What is half of 72 in math?

Answers

Answer:

36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Divide 72 by 2, and you get 36

What is the radian equivalent for 180°? 2 pi radians pi radians startfraction pi over 2 endfraction radians

Answers

Answer:

180° = pi radians

Step-by-step explanation:

360° = 2pi radians

90° = pi/2 radians

see image

180° is pi radians.

pi radians is equivalent to 180 degrees, option B is correct.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The radian equivalent of 180° is pi radians.

This is because a full circle is 360°, which is equivalent to 2 pi radians. Therefore, half of a circle or an angle of 180° is equivalent to half of 2 pi radians, which is pi radians.

Hence,  pi radians is equivalent to 180 degrees, option B is correct.

To learn more on trigonometry click:

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On Monday, Andrew ate some grapes. On Tuesday, he ate 2 more grapes than what he ate on Monday. On Wednesday, He ate 2 more grapes than what he ate on Tuesday. Each day of that week he ate 2 more grapes than what he ate the day before. By the end of Friday, He had eaten 30 grapes in total. How many grapes did Andrew eat on Monday?

Answers

Answer: I think It's 38

Step-by-step explanation:

you can multiply or add all of them together

Answer: Andrew ate 22 grapes on Monday.

Step-by-step explanation:

From Monday to Friday it is 4 days. since he ate 2 more grapes every day. You multiply 2 by 4. To get 8 and subtract 30 by 8 to get 28.

Which two terms in (3+14) +27 could you add to get a multiple of ten? ​

Answers

Answer:

3 and 27

Step-by-step explanation:

Step 1:  Determine which two terms we can use

We have the following numbers to choose from:  3, 14, 27

Adding two numbers to get a multiple of ten means that the number that we come up with needs to be divisible by ten.  For example:  20, 30, 50, 100 are all multiples of ten.

In this example the only one that would add up to create a multiple of ten is 27 and 3 which would give us 30 which is a multiple of 10.

Answer: 3 and 27

Find the value of x


x =

Answers

Answer:

[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the value of x.}[/tex]

[tex]\textsf{The value of x is an angle for this triangle.}[/tex]

[tex]\textsf{Note that we are given 2 other angles, we can use what is given to us to solve for x.}[/tex]

[tex]\large\underline{\textsf{What is a Triangle?}}[/tex]

[tex]\textsf{A Triangle is a shape with 3 sides, and 3 angles. Sometimes these can be congruent,}[/tex]

[tex]\textsf{other times, and most of the time they're not. These are called Equilateral}[/tex]

[tex]\textsf{Triangles. Every Triangle consists of 3 angles that add up to 180}^{\circ}. \ \textsf{If the angles}[/tex]

[tex]\textsf{don't add up to 180}^{\circ}, \ \textsf{then the shape is not a triangle.}[/tex]

[tex]\textsf{Now that we know a Triangle has 3 angles that add up to 180}^{\circ}, \ \textsf{we can create an}[/tex]

[tex]\textsf{equation where x is the \underline{subject}.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{All 3 angles add up to 180}^{\circ}, \ \textsf{let's create an equation.}[/tex]

[tex]\tt 180^{\circ} = 37^{\circ} + 53^{\circ} + x^{\circ}[/tex]

[tex]\textsf{To make x the subject, move x to the other side of the equation by subtracting x.}[/tex]

[tex]\tt 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} + x^{\circ} - x^{\circ}[/tex]

[tex]\textsf{We should also move 180}^{\circ} \ \textsf{to the other side of the equation as well.}[/tex]

[tex]\tt 180^{\circ} - 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} -180^{\circ}[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}[/tex]

[tex]\textsf{We should remove the negative for x by dividing the whole equation by -1.}[/tex]

[tex]\frac{\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}}{-1} \rightarrow \tt x^{\circ}= 180^{\circ} - 37^{\circ} - 53^{\circ}[/tex]

[tex]\underline{\textsf{Simplify the right side of the equation;}}[/tex]

[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]

2. Which expression is equivalent to 3x - (2x+4)+5?
b. x+9
c. 5x+9
d. 5x+1

Answers

Answer:

x + 1

Step-by-step explanation:

[tex]3x - (2x+4)+5[/tex]

[tex]3x-2x-4+5[/tex]

[tex]3x-2x+1[/tex]

[tex]x+1[/tex]

The answer to your question is D.

Suppose that there are two types of tickets to a show advance and same day the combined cost of one advance ticket and one same-day ticket is $70 for one performance 20 advance tickets and 35 same day tickets were sold.The total amount paid for the tickets was $1850.what was the price of each kind of ticket

Answers

The price of the advance ticket is  $40 and the price of the same day tickets is $30.

What are the linear equations that reperesent the question?

a + b = $70 equation 1

20a + 35b = 1850 equation 2

Where:

a = cost of one advance ticket

b = cost of one same day ticket

What is the cost of one same day ticket?

Multiply equation 1 by 20

20a + 20b = 1400 equation 3

Subtract equation 3 from equation 2

15b = 450

Divide both sides by 15

b = $30

What is the cost advance ticket?

Subtract $30 from $70.

$70 - $30 = $40

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Harper has a bag that contains apple chews, cherry chews, and lime chews. She
performs an experiment. Harper randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Harper performs the experiment 38 times.
The results are shown below:
An apple chew was selected 22 times.
A cherry chew was
selected 6 times.
A lime chew was selected 10 times.
Based on these results, express the probability that the next chew Harper removes
from the bag will be lime chew as a percent to the nearest whole number.

Answers

We can use the results from Harpers experiment to find the probabilities of any of the chews. We don’t need to know the actual number of chews nor do we need to know the number of each type.

The question says that out of the 38 chews taken out of the bag, 10 of them were lime chews. All we need to do to answer this question is to put that into a percentage. We can do this by doing 10/38 and then multiplying by 100. This will give 26.32%. Since we want this to the nearest whole number we will round to 26%.

Hope this helps

Find the side ratio given
pls show work<3 :)

Answers

Answer:

5/2    See below

Step-by-step explanation:

L x W x H = 125/8

for a CUBE   L   W and H are the same

L^3 = 125/8

L = 5/2

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