Arithmetic and Geometric Sequences

1. Consider the sequence: 3, 7, 11, 15...

Find an explicit formula for the n-th term of this sequence.

Answers

Answer 1

Answer:

Step-by-step explanation:

This is arithmetic since adding 4 to each term gets us to the next term in the sequence. That means that the common difference, d, is 4. The general arithmetic explicit formula is

[tex]a_n=a_1+d(n-1)[/tex] and using the info given when a1 = 3 and d = 4:

[tex]a_n=3+4(n-1)[/tex] or, if you want to make it easier to deal with:

[tex]a_n=4n-1[/tex] (I just distributed through the parenthesis and then combined like terms. As you can see, arithmetic sequences are linear).


Related Questions

Which of the following values is a solution for the inequality statement?
Select all that apply.
-5 ≤ -4r + 3

A.7
B. 4
C. -5
D. 0
E. 3

Answers

Answer: C and D
(the solution is r is less than or equal to 2)

Answer:

-5 and 0

Step-by-step explanation:

The vertex form of the equation of a parabola is y=(x-5)+16. what is the standard form of the equation

Answers

Answer:

x − y =  − 11

Step-by-step explanation:

Can someone help me with this? Will Mark brainliest.

Answers

You're answer is Major Arc.

I am a multiple of 30, if you round me to the nearest hundred, you can get 400, what number could I be? *

Answers

Answer and Step-by-step explanation:

The answer can be 360 or 390, as both of these can round up to the nearest hundred and become 400.

#teamtrees #PAW (Plant And Water)

Alright I need help again and I will award brainliest if you are correct

Answers

Answer: No Triangle: 30 , 85 , 60, and 2, 8, 10

One Triangle: 7, 24, 25

Many Triangles: 45, 45, 90           5, 15, 160

Is he correct or not ?

Question 10 of 10 Classify the following triangle. Check all that apply. 7 A. Right B. Acute C. Isosceles D. Scalene E. Equilateral F. Obtuse​

Answers

D & F

Step-by-step explanation:

D scale because all sides are different lengths

F obtuse because one angle is greater than 90 degrees

Look up definition of the other properties and you will see they don't apply

The given triangle is a obtuse and scalene triangle

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangle is an obtuse triangle and scalene triangle.

A triangle whose any one of the angles is an obtuse angle or more than 90° is known as obtuse triangle.

A triangle in which all the three sides have different lengths then it is called as scalene triangle.

Hence, the given triangle is a obtuse and scalene triangle.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ5

Complete the function for this graph.

Answers

Answer:

1 and 4

Step-by-step explanation:

The vertex of the graph is (1,4) which is translated up 4 units

What is m angle KNL?
Enter your answer in the box.​

Answers

Answer:

KNL = 102

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

5x+2 = 3(x+14)

5x+2 = 3x+42

Subtract 3x from each side

5x-3x+2 = 3x+42-3x

2x+2 = 42

Subtract 2 from each side

2x+2-2 = 42-2

2x = 40

Divide by 2

2x/2 = 40/2

x = 20

We want to find KNL

KNL = 3(x+14) = 3(20+14) = 3 ( 34) = 102

1) $50,000 is invested at a rate of 3% compounded monthly for 6 years.please answer as equation ​

Answers

Answer:

9,000

Step-by-step explanation:

formula= I=prt

turn 3% into a decimal

x=(50k)0.03(6)

x=9000

correct me if im wrong but this should be correct

Situation: Find the substance's half-life, in days. Round your answer to the nearest tenth. A 33 gram sample of a substance that's used for drug research has a k-value of 0.1081. Enter the correct answer. N = Noe DONE No = initial mass (at time t = 0) 000 OO N = mass at time t k= = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days​

Answers

Answer:

1051 or..

10.51

Step-by-step explanation:

Since 33=30 and 0.1081 is supposed to be as a percentage since its already a  decimal you could just round it and make it into a fraction then once you get the answer to the fraction it would either be 1081 since 0.1081 as a fraction is 1081/10000 or you could make into 10.81 as a decimal but after that you subtract "30 - 1,081" or 10.81 -30" either one of them and each of those numbers would give you the same exact number. Answer: 1051 or as a decimal 10.51

Answer:

The correct answer 6.4 on PLATO edmentum

Step-by-step explanation:

I did the test

Q. Find missing angle

Answers

Answer:

c =√a2 + b2=√152 + 122=√369=19.20937

∠α =arcsin(a)c= arcsin(15)19.209372712299=arcsin(0.78086880944303) = 51.34° = 51

answer is C

Answer:

Tan x = opp/ adj

Tan x = 15 / 12

Tan x = 1.25

Angle = 51.34

C. 51 degrees

HOPE ITS HELPS..!!

how would u get the solution to x/3 < -2

Answers

by doing the math ;)

Brian asked a group of people their favourite country . The results are summarised in the table. Destination UK Europe USA Africa Other
48 72 72 144 144

Answers

Answer:

I don’t really understand but here’s the table;

Step-by-step explanation:

UK = 48

Europe = 72

USA =72

Africa = 144

Other = 144

Answer:

ok so heres what that would look like

UK:48

Europe:72

USA:72

Africa:144

Other:144

Total:480

Which of the following equations is equivalent to 5(2p – 6) = 40?
10p – 6 = 40
7p – 11 = 40
10p – 30 = 40
7p – 1 = 40

Answers

10p-30=40 is equivalent to 5(2p-6)=40

This is because you have to distribute 5 to 2p and negative 6

So 5 times 2p is 10p and 5 times -6 is -30

When you put this all together you get 10p-30=40
Answer: 10p-30=40

Explanation: In this question, you are asked to distribute to find an equivalent equation. When you distribute, you multiply the term on the outside of this equation with the terms on the inside. In this case, you needed to multiply 5•2p and 5•-6. Then, you need to put them together to create the equation. These terms will be on the left side of the equation, while 40 will remain on the right side. Once multiplied, you should get 10p and -30. Your final equation will be 10p-30=40.

Hope this helps! Comment below for more questions.

Find the value of g in the figure given below.
Assume that the lines are parallel.

Answers

Answer:

d=60-degree (Vertically opposite angles)

e=d=60-degree (Alternate angles)

e+g=180-degree (Being in a straight line)

60+g=180

g=180-60

g=120-degree

Answer:

angle g = 20 degree

Step-by-step explanation:

60 degree + angle g = 180 degree (being co exterior angles)

angle g = 180 - 60

angle g = 120 degree

Note : co interior angles are the angles formed on the exterior of the two parallel lines and which are on the same side of the transversal  .

The volume of a cylinder is 156 pi centimeters cubed. What is the volume of a cone with the same base and height as the cylinder?

Answers

Answer:

52 pi centimeters cubed

Step-by-step explanation:

volume of a cylinder = πr^2h

Volume of a cone 1/3(πr^2h)

π = 22/7

r = radius  

The volume of a cone is one-third that of a cylinder

volume of cone = 156/3 = 52

Find the value of x ?

Answers

4x-1 = 3x+3 ——> 4x=3x+4 ——> 1x= 4——> x=4 then plug it in to test and both get 15

2) In a class of 31 students, some study Physics and some study Chemistry. If 22
study Physics, 20 study Chemistry and 5 study neither. Calculate how many take:
a) both Physics and Chemistry
b) just Physics
c) just Chemistry

Answers

I believe the answer is C

6 = r + 2 Addition and Subtraction Equations 11.2

Answers

Answer:

I'm not sure what you are looking for but I'm assuming you are finding r.

r is equal to 4.

Step-by-step explanation:

6 = r + 2

In order to find r, you have to subtract 2 from 6.

So, r = 6 - 2 = 4

SOMEONE PLEASE HELP ASAP!!

Answers

Answer:

YES SIR!

Step-by-step explanation:

its

x=4    y=6

x= 6 y=9

Answer:

4, 6

6, 9

Step-by-step explanation:

give a definition for each of the following terms. are there other terms that need to be defined first? what are they and how might you define them?
(i) parallel lines
(ii) perpendicular lines
(iii) line segment
(iv) radius of a circle
(v) square​

Answers

Step-by-step explanation:

espero que te ayude amigo

I need help with this problem. please help. thanks

Answers

Answer:

D

Step-by-step explanation:

Answer:

Option B. ( For Question 32...)

Step-by-step explanation:

14. A cellular telephone company recently conducted research into the length of calls (in
minutes) made by customers. In a random sample of 30 calls, the sample mean was
x= 18.6 minutes and the standard deviation was s=5.2 minutes. Construct and interpret
a 90% confidence interval for true mean call length. (4-step process)

Answers

Answer:

The correct answer is "16.987, 20213".

Step-by-step explanation:

Given that,

[tex]n=30[/tex]

[tex]\bar x=18.6[/tex]

[tex]s = 5.2[/tex]

[tex]df=30-1[/tex]

   [tex]=29[/tex]

[tex]\alpha = 0.10[/tex]

By using the table, the critical values of t will be:

= [tex]\pm 1.699[/tex]

Now,

The confidence interval will be:

= [tex]\bar x \pm \frac{t\times s}{\sqrt{n} }[/tex]

By putting the values, we get

= [tex]18.6 \pm \frac{1.699\times 5.2}{\sqrt{30} }[/tex]

= [tex]16.987,20.213[/tex]

4. A rental car agency charges a fee of $25 plus $0.20 for every mile driven. Write a function rule to determine the cost of renting a car.
a. What is the cost of driving a rental car 150 miles?
b. If I have $145, how far many miles can I drive the rental car?
Besties help please

Answers

Answer:

a. $25 + ($0.20 × 150) = $25 + $30 = $55

b. $145 ÷ $0.20 = 725 miles

Evaluate the expression 33.15/n n=1.5

Answers

Answer:

22.1

Step-by-step explanation:

33.15/n

33.15/1.5

= 22.1

Which area model can u use to fine * find 39 x73

Answers

The area model you can use is D , cs 70 +3 & 30+9

the mid point of the sides of a triangle are (1,5,-1),(0,4,-2),(2,3,4) find the vertices​

Answers

Answer:

Step-by-step explanation:

The equation p=100−5t represents the percent p of battery power remaining in a tablet after t hours.

a. Identify the independent and dependent variables. Then describe how the battery power changes over time.

The independent variable is
and the dependent variable is
.

The battery power begins at
% and decreases
% each hour.

Question 2
b. Graph the equation.

Answers

Answer:

a) Independent variable is the hours.

Dependent variable is the power left after t hours

b) The graph that shows in the images

*sorry if my answer is wrong

Im stuck on this hegarty maths question help me please

Answers

Answer:

540 g flour

4 tsp baking powder

8 tbsps sugar

520 mL milk

4 eggs

8 tbsps oil

Step-by-step explanation:

Multiply each ingredient by 4!

Because the initial recipie provides the amounts for 6, simply divide 24/6 and you'll find that you only need 4x the original recipie.

135g*4 = 540

1 tsp*4 = 4 etc!

Find AB using the segment addition postulate.

Answers

Answer : AB = 12

Explanation:

2x + 6 + 5x - 3 = 24
7x + 3 = 24
x = 3

AB = 2x + 6 = 2(3) + 6 = 12
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