If the sum of the first nterms of an AP is 3 + 4n2.Find the 3rd, the 10th andthe nth terms.

Answers

Answer 1
Given:

Sum of first n terms of an AP – Sn = 3 + 4n²

Find:

the 3rd, the 10th andthe nth terms.

Solution:

Substitute the value of n as 1 to find the first term of the given AP.

(Sum of first 1 terms is nothing but the first term).

Hence,

⟹ S₁ = a = 3 + (4)(1)²

⟹ a = 3 + 4

⟹ a = 7

Now,

Substitute the value of n as 2 to find the sum of first 2 terms.

⟹ S₂ = a + a₂ = 3 + 4(2)²

⟹ a + a₂ = 3 + 16

Substitute the value of a here.

⟹ 7 + a₂ = 19

⟹ a₂ = 19 - 7

⟹ a₂ = 12

We know,

nth term of an AP – an = a + (n - 1)d

So,

a₂ = a + (2 - 1)d = a₂ = a + d.

Subtract a from a₂.

⟹ a + d - a = 12 - 7

⟹ d = 5

Now,

nth term = an = 12 + (n - 1)(5)

⟹ an = 12 + 5n - 5

⟹ an = 5n + 7

Substitute n as 3 & 10 , to find the 3rd & 10th terms.

★ a₃ = 5(3) + 7

⟹ a₃ = 8 + 7

⟹ a₃ = 15

★ a₁₀ = 5(10) + 7

⟹ a₁₀ = 50 + 7

⟹ a₁₀ = 57

Therefore,

Third term is 15

Tenth term is 57

nth term is 5n + 7.

I hope it will help you.

Regards.

Answer 2

Step-by-step explanation:

please see the attachment

If The Sum Of The First Nterms Of An AP Is 3 + 4n2.Find The 3rd, The 10th Andthe Nth Terms.

Related Questions

graph y = 5/3x - 9 please

Answers

Answer:

hope this helps :)

Step-by-step explanation:

brainliest if correcto

A car dealership manager has determined that the prot, in thousands of dollars, of the dealership can be determined by the expression , where is the number of cars sold. A dierent manager states that the prot of the dealership can be determined by the function . What number of cars sold makes the equation true? Select all that apply

Answers

A car dealership manager has determined that the profit, in thousands of dollars, of the dealership can be determined by the expression LaTeX: x^2-4xL a T e X : x 2 − 4 x, where LaTeX: xL a T e X : x is the number of cars sold. A different manager states that the profit of the dealership can be determined by the function LaTeX: 5xL a T e X : 5 x. What number of cars sold makes the equation LaTeX: x^2-4x=5xL a T e X : x 2 − 4 x = 5 x true? Select all that apply.

Answer:

x = 0 ; x = 9

Step-by-step explanation:

Given that:

Manager 1 's profit function:

x² - 4x ; x = number of cars sold

Manager 2's profit function:

5x ; x = number of cars sold

Nunbers That makes the equation:

x² - 4x = 5x true

x² - 4x = 5x

Subtract 5x from both sides to make right hand side =. 0

X² - 4x - 5x = 5x - 5x

x² - 9x = 0

Using factorization to equate separate the x values.

x(x - 9) = 0

x = 0 or (x - 9) = 0

Hence,

x = 0 ; or

x - 9 = 0 ; x = 9

x = 0 OR x = 9

Number of cars sold which makes both managers have the same profit from the functions are either 0 or 9

i truly need help with this

Answers

i think you multiply 14 and 52 or divide one of those i’m pretty sure

5(7a + 5)
simplify your answer

Answers

Answer:

35a+25

Step-by-step explanation:

You distribute the 5 to the 7a & the 5 inside the parenthases.

A consumer spends all of his money on two goods: apples and oranges. The consumer will pay $10 for apples, but only $1 for oranges. Why does the consumer pay more for apples?

Answers

Answer:

Step-by-step explanation:

Since no further information is given in this question the only reason a consumer would spend more on one item than the other is purely because of preference. The consumer in this scenario seems to enjoy eating or needs apples much more than he enjoys eating or needs Oranges. Therefore, he is ok with spending more money and getting a larger quantity of Apples than Oranges. This all depends on the demand that the individual has for a specific item over another item.

I NEED HELP ASAPP!!!!

Answers

Answer: 156 divide 15 = 10.4

Step-by-step explanation:

Miss Owens plans to join golds gym there is a one time registration fee of $75 and a monthly charges $15 write an equation to represent the situation. Be sure to identify the slope and the Y intercept remember your equation must be in slope intercept form

Answers

Answer:

y=15x+75

hope this helps!

Question 5 of 5
Which relation is not a function?

Answers

Answer:

Step-by-step explanation:

I think its c

I think it is c. B is wrong

help please ill give brainliest

Answers

The angle is a right angle so therefore you can use Pythagorean theorem to find the value of hypotenuse x.

Theorem:
a^2+b^2=c^2, with C representing hypotenuse.

Substitute numbers:
7^2 + 3^2 = c^2
49+9=c^2
58=c^2
Square root to isolate c. Radical 58 is your answer.

who wants this name for free?

Answers

Answer:

What do you mean?

Step-by-step explanation:

Answer: someone else can have it, but thanks

Step-by-step explanation:

What is the slope and y-intercept of the equation below?
3x - 2y = 6

Answers

Slope: 3/2
Y-intercept: -3

answer:

the slope is: 3 over 2

the y intercept is: negative 3

explanation:

hope this helped <3 also if wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)

Let a represent an unknown number. If 33 is 11 more than a, which equation can be used to find a?

33 + 11 = a
33 – 11 = a
33 × 11 = a
33 ÷ 11 = a

Answers

The answer is 33 - 11 = a

Answer:

33-11=a

Step-by-step explanation:

3-11=22  so a =22 , so 22 equals a. this makes a 11 less than 33.  33-22=11 so a has to equeal 22

describe a real life multiplication situation for wich an estimate makes sense

Answers

Answer and step-by-step explanation:

Let's say for example that you want the circumference of a car tire to be a certain size, but the company only sells the measurements in the tire's radius. The formula for circumference is 2 * pi * r. We know that pi is not a rational number, so an estimate is required. The car tire you want is 6.5 inches in it's radius, and you want to see what the circumference is. Firstly, let's substitute the r in our equation. Then the equation becomes 2 * pi * 6.5. Then let's solve. Let's change our equation to 2 * 6.5 * pi to save the irrational part for last. Then our equation is 13 * pi. Lastly, let's round pi to 3.14, since we can only estimate its irrationalness. We get 40.82 inches. This is an example that you might use in real life while multiplying and estimating. I hope this helps, I hope it's not wrong, but I do not think it is.

please help me with this.

Answers

Answer: Choice B) 74

Explanation:

The two parallel lines form a parallelogram.

For any parallelogram, the opposite angles are congruent.

So the angle adjacent to P is also 106 degrees.

The adjacent angles add to 180

P+106 = 180

P = 180-106

P = 74

Which pairs of points would result in a line with a rate of change of 2.1? Select all that apply.
A. (-4,11) and (-2,7)
B. (5, 6) and (-5, 12)
C. (0,3) and (-4,11)
D. (0, – 3) and (5, 7)

Answers

Answer: A, C and D

Step-by-step explanation:

Let us find the slope(rate of change ) of each pair of points

The slope formula is

Plug in the points (− 4 ,− 11 ) and (-2 , − 7) to get;

The rate of change of this pair 2:1

For B part, we plug the points ( 5 , 6 ) and ( − 5 , 12 )

The rate of change is NOT 2:1

For part C, we plug in ( 0 , − 3 ) and ( − 4 , − 11 )

The rate of change of this pair is also 2:1

For part D, we plug in (0 , − 3) and ( 5 , 7 )

This also has rate of change to be 2:1


What is the slope of the following table?

Answers

Answer:

The slope is 2.5

Step-by-step explanation:

7-2=5. 4-2=2

5/2=2.5

What is the measure , in degrees of the angle marked B?

Answers

Answer:

B = 142

Step-by-step explanation:

First, you need to find the angle of the third angle of the triangle. The three angles of a triangle always add up to 180, so it will be:

n + 77 + 65 = 180

= n + 142 = 180

= n = 38

Now, you need to find the angle supplementary to 38, as 38 and B are linear angles. Two supplementary angles add up to 180, so:

B + 38 = 180

= B = 142

The measure of the angle marked as B that is ABD in the given figure is equal to 142°.

Let us consider the vertices of the triangle are A, B , C

Where

measure of angle A = 77 degree

measure of angle C = 65 degree

Ray CB extends to Point D such that C-B - D.

Sum of all the interior angles in a triangle is equal to 180 degree.

Let measure of angle ABC be x degree.

m∠ABC + m∠BAC + m∠BCA  = 180°

⇒ x° + 77° + 65° = 180°

⇒ x° + 142°= 180°

⇒ x° = 38°

Now angle ABC and angle ABD are linear pair.

m∠ABC + m∠ABD = 180°

⇒ 38° + m∠ABD = 180°

⇒ m∠ABD = 180° - 38°

⇒ m∠ABD = 142°

Therefore, measure of the angle marked as B is equal to  142°.

learn more about angle here

brainly.com/question/30147425

#SPJ2

How Many Miles Is A Race That Is 12 Laps Around A 1/2- Mile Track?

Answers

Answer:

12 Miles is the answer! Hope you do Great!

Step-by-step explanation:

Simplify the expression: 3x+2(x+6)-4-2x

Answers

Answer:

3x+8 is the simplest you can get to

Step-by-step explanation:

Answer:

3x+8

Step-by-step explanation:

3x+2(x+6)-4-2x

Apply the distributive property

3x+2x+12-4-2x

Combine Like Terms

3x+8

find the sum 1/2 + (-3/4)=

Answers

Answer:

I think this is the answer

-0.25

Step-by-step explanation:

2-3/4

-1/4

The answer is -1/4 and this is step by step

Mark and Jane had 95 stamps. After Mark gave 35 stamps to Kevin, Mark and Jane had same number of stamps. How many stamps did Mark have at the beginning?

Answers

95 - 35 = 60
60/2 = 30
35 + 30 =65
Mark had 65 stamps at the beginning.

What inequality represents this graph?

Answers

Answer:

x ≥ -8

General Formulas and Concepts:

If it is a closed dot, we use the inequality and equal sign: ≥ or ≤

If it is a open dot, we use the inequality only: > or <

Step-by-step explanation:

We can label the solutions as x.

We see starting from -8 that are solutions get larger.

Since the dot is closed, we use the greater than or equal to sign: ≥

Therefore, x has to be greater than -8 and increasing towards ∞.

x ≥ -8

When is it best to find the average of the entire population? Select all that apply.

A)when there is a small amount of data in the population
B)when there is a large amount of data in the population
C)when it is easy to access the data set of the population
D)when it is hard to access the data set of the population
E)when there is no time to perform the calculations

Answers

Answer:

Step-by-step explanation:

im guessing probably E

I hope im right

Answer: when there is a small amount of data in the population.

Find the measure of the angle indicated in the bold type

Answers

Answer:

94 degrees

Step-by-step explanation:

So you set those equations equal to 180 to find x.

14x+10+15x-4= 180

29x+6= 180

29x= 174

x=6

So now that x=6, you plug it in to find the bold angle.

14(6)+10

84+10

= 94

Find the value of n for the regular n-gon described.
Each interior angle of the regular n-gon has a measure of 75.2º.

Answers

Answer:

n = 3.44

Step-by-step explanation:

The interior angle of a regular n-gon is given by the formula;

[tex] I = \frac {180(n-2)}{n} [/tex]

Where,

I represents the interior angle. n represents the number of sides.

Given that interior angle = 75.2°

Substituting into the equation, we have;

[tex] 75.2 = \frac {180(n-2)}{n} [/tex]

Cross multiplying, we have;

[tex] 75.2n = 180(n-2)[/tex]

[tex] 75.2n = 180n - 360[/tex]

Rearranging the equation, we have;

[tex] 180n - 75.2n = 360[/tex]

[tex] 104.8n = 360[/tex]

[tex] n = \frac {360}{104.8}[/tex]

n = 3.44

Therefore, the number of sides "n" of the regular n-gon described is 3.44.

EASY - 2nd part
Need the following would you rather questions to be answered for a survey, need 5 people to answer
1) Would you rather be on house arrest or go to jail for a month?
2) Would you rather go to court and plead guilty or be placed on probation for 10 months?
3) Would you rather clean garbage alongside the road or speak to schools?
4) Would you rather go to solitary confinement for a year, or go to regular prison for 10?
5) Would you rather spend a half a lifetime in prison or a lifetime on probation?

Answers

Answer:

1. House arrest

2. Probation for 10 months

3. Speak to schools

4. Regular prison for 10 years

5. Lifetime on probation

Answer:

ok

Step-by-step explanation:

1) House Arrest!

2) Court

3) Speak to School's

4) Solitary

5) Probation

0-0

PLEASE HELP WILL GIVE BRAINIEST

Answers

Answer:

3

Step-by-step explanation:

solve for f.
f - 518 = -147
f = ?
please help

Answers

Answer:

f = 371

Step-by-step explanation:

Just add 518 to both sides this dumb easy

what s 1 +2 i forgot

Answers

Answer:

3 is te anwer jajajaj thanks u

so if u-6=-3 does that mean u equals 9?

Answers

Answer:

False.

Step-by-step explanation:

u = 3

Isolate the variable, u. Note the equal sign, what you do to one side, you do to the other. Add 6 to both sides of the equation:

u - 6 = -3

u - 6 (+6) = -3 (+6)

u = 6 - 3

u = 3

~

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