The seventh term of an arithmetic progression is equal to twice the fifth term. The sum
of the first seven terms is 84. Find the first term.

Answers

Answer 1

Answer:

a₁ = - 24

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₇ = 2a₅ , then

a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )

- a₁ - 2d = 0 → (1)

The sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

Given [tex]S_{7}[/tex] = 84 , then

[tex]\frac{7}{2}[/tex] (2a₁ + 6d) = 84

3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )

2a₁ + 6d = 24 → (2)

Thus we have 2 equations

- a₁ - 2d = 0 → (1)

2a₁ + 6d = 24 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate d

- 3a₁ - 6d = 0 → (3)

Add (2) and (3) term by term to eliminate d

- a₁ = 24 ( multiply both sides by - 1 )

a₁ = - 24


Related Questions

How many 1/8s are in 1 1/4

Please answer

Answers

Answer:

10

Step-by-step explanation:

Two 1/8 is a quarter

1/8 in decimal form is 0.125

0.125 x 10 = 1.25 a.k.a 1 1/4

I'm so sorry for the mistype

Answer:

Step-by-step explanation:

One eighth is one part of eight equal sections. Two eighths is one quarter and four eighths is a half. Eighths if you make them into quarters and then divide each quarter in half.

80 inches of snow over 10 days what is the rate and unit rate

Answers

Answer:

The rate is 80 in. : 10 days

The unit rate is 8 in. : 1 day

Step-by-step explanation:

Divide 80 by 10, you get 8 which is the amount of snow you would get in 1 day.

Amelia and her brother had a snow day, so they played in the snow for 3 hours. During that time, it snowed another 4.8 inches. If the snow fell at a steady pace, how much snow fell each hour?

Answers

Answer:

1.6

Step-by-step explanation:

The amount of snow fell each hour is 1.6 inches per hour.

What is Unit Rate?

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity

Given that,

Time Amelia and her brother played in the snow = 3 hours

Amount of snow fell at that time = 4.8 inches

That is 4.8 inches of snow per 3 hours

We have to calculate the unit rate of the amount of snow falling in an hour.

Amount of snow in 1 hour = 4.8 / 3 = 1.6 inches per hour

Hence the 1.6 inches of snow is falling per hour.

To learn more about Unit Rate, click on the link :

https://brainly.com/question/11258929

#SPJ2

What is the solution to this inequality?
X10
+7 > 10
A. X2 27
B. xs 83
C. xs 27
D. x2 83

Answers

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[tex] \frac{x}{9} + 7 \geqslant 10 \\ [/tex]

Subtract sides 7

[tex] \frac{x}{9} + 7 - 7 \geqslant 10 - 7 \\ [/tex]

[tex] \frac{x}{9} \geqslant 3 \\ [/tex]

Multiply sides by 9

[tex]9 \times \frac{x}{9} \geqslant 9 \times 3 \\ [/tex]

[tex]x \geqslant 27[/tex]

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Thus the correct answer is (( A )) .

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f(x) = -3/(2x-1) find the largest possible domain

Answers

There is no domain
Pls mark brainliest

The middle question. Any help would be nice

Answers

Answer:

"Nothing but net" won the game

Step-by-step explanation:

Answer:

they won

61 to 43

Step-by-step explanation:

EMERGENCY! Please give me the correct answer!​

Answers

Sorry luv I’m doing a test I need points
1/4

it would be 2^-2

Pls someone help me please

Answers

2

1

3

5/8 = 0.625

1/3 = 0.3333...

17/24 = 0.70833333

round 79.6 to the nearest whole number

Answers

Answer:

80

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Need help with this problemm

Answers

Answer:

60

Step-by-step explanation:

It is because all angles in an equilateral triangle add up to 180 degrees meaning that they are all equal. You can know its an equilateral triangle from the small lines an the sides meaning they are equal.

what are the common factors of 20 and 30
A. 1,2,5,10
B. 1,2,10
C. 1,10
D. 1,5,10

Answers

Answer:

D.

Step-by-step explanation:

Its D. Bruh

PLEASE HELP!!!!! Match each equation with its slope





(I also have another question like his in my profile)

Answers

Answer: 1. E

2. B

3. C

4. F

5. D

6. A

Step-by-step explanation:

4x – x + 8 ≤ 35
What’s the answer

Answers

3x is less than or greater to 27 is what I got

Answer:

x ≤ 9

Step-by-step explanation:

4x – x + 8 ≤ 35

3x + 8 ≤ 35

3x ≤ 27

x ≤ 9

Use the diagram and the given angle measure to find the other three measures.

m∠1=143∘

m∠2=

m∠3=

m∠4=

Answers

Answer:

angle 2 = 37⁰

angle 3 = 153⁰

angle 4 = 37⁰

Step-by-step explanation:

I guess this refers to two intersecting lines which form 4 angles.

Angles 1 and 2 are supplementary angles whose sum is 180⁰.

Angle 1 + angle 2 = 180⁰

143⁰ + angle 2 = 180⁰

angle 2 = 180⁰ - 143⁰

angle 2 = 37⁰

Angles 1 and 3 are vertical angles so do with angles 2 and 4. Therefore it is easy to find their measures because vertical angles are congruent in measures.

Hope this helps...

Answer:

m∠1 = 143°

m∠2 = 37°

m∠3 = 143°

m∠4 = 37°

At the supermarket, you can fill your own honey bear container. A customer buys 12 oz of honey for $5.40.
How much does honey cost per ounce?
How much honey can you buy per dollar? Round to the nearest hundredth.

Answers

Answer: a. $0.45; b. 2.22 oz

Step-by-step explanation:

From the question, we are informed that acustomer buys 12 oz of honey for $5.40.

a. How much does honey cost per ounce?

To calculate this, we divide $5.40 by 12oz. This will be:

= $5.40/12

= $0.45

b. How much honey can you buy per dollar?

Since 1 ounce cost $0.45, the number of honey that can be bought for $1 will be:

= $1/$0.45

= 2.22 oz

I drive at 55 miles per hour, and my trip will takr 5 hours. Proportional or non proportional

Answers

Answer:

Proportional

Step-by-step explanation:

Here, we want to know if the distance at the given time will be proportional

What we will do here is to simply divide the distance by the time

Mathematically, that will be 55 miles/ 5 hours = 11 miles / hour

So this means that in an hour, 11 miles will be traveled

This expression is proportional

State the solutions of the equation |x| + 2 = 4.

Answers

I think thats 2

Because 2+2=4

answer: 2 and -2

explanation: if you plug in 2 or -2 or x, then it would always become 2. this is because if you take the absolute value of any number, then it would become positive. this makes the equation true because 2 + 2 = 4

HELP MATH QUESTION!!

Answers

Answer:

The last answer is correct

Step-by-step explanation:

there is a 10 point slope in between 13 and 3

find the equation of the line that passes through a and b

Answers

Answer:
y = 2x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = A(4, 7) and (x₂, y₂ ) = B(2, 3)
m = = = 2, thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation.
Using B(2, 3), then
3 = 4 + c ⇒ c = 3 - 4 = - 1
y = 2x - 1 ← equation of line

can you solve this problem

Answers

Answer:

78 people were originally on the boat

Step-by-step explanation:

Answer:

78 people started on the boat

Step-by-step explanation:

let America be America meaning

Answers

Answer:

Let America be America Again Analysis In Langston Hughe's poem “Let America be America Again” he talks about how America should return to the way that it was perceived to be in the dreams before America was truly America. Throughout the poem, he uses various methods to evoke the patriotic images and dreams that he feels America should and will eventually be. Hughes states that America is supposed to be a place of equality for everyone including both white and colored people.

Step-by-step explanation:

If it was helpful can I plz have a brainliest

The function f (x) = 6x + 13 defines a
sequence for x > 1. What are the first three
terms of the sequence?

Answers

Answer:

15, 21, 27

Step-by-step explanation:

Given the function :

f(x) = 6x + 13 ; which defines a sequence for x > 1

The first three terms of the sequence ;

x > 1 ;

Hence x = 2, 3, 4

The sequence :

f(2) = 6(2) + 3 = 12 + 3 = 15

f(3) = 6(3) + 3 = 18 + 3 = 21

f(4) = 6(4) + 3 = 24 + 3 = 27

While making desserts for a bake sale, Steve used 5/6 of a scoop of brown sugar as well as 1/6 of a scoop of white sugar. How much more brown sugar did Steve use?

Answers

Answer:

5/6 - 1/6 = 4/6 = 2/3

Step-by-step explanation:

Since both numbers' denominators are the same, all you have to do is minus normally on the top numbers. You would take the difference and put it on the same denominators. Finally simplify!

do positive numbers have negative square roots?

Answers

Yes. They have two square roots. Both have the same absolute value but one is positive while the other is negative.

A pair of jeans was 25% off the original price. The sale resulted in a $24 discount. What was the original cost of the jeans before the sale?

Answers

Answer:

The original cost of the jeans before the sale was 30$

Step-by-step explanation:

In triangle QRS, angle Q measures 33.7°, angle R measures 52.3°, and angle S measures 94º. Based on the information that is provided, which could be a correct set of sides for this set of angles?

O side QR = 7 cm. side RS = 10 cm , side QS = 12.6 cm

O side QR = 10 cm, side RS = 7 cm, side QS = 12.6 cm side

O QR = 12.6 cm, side RS = 10 cm, side QS = 7 cm

O side QR = 12.6 cm, side RS = 7 cm, side QS = 10 cm​

Answers

You know, it's easier to draw it out to figure out the answer!

It's side QR = 12.6 cm, side RS = 7 cm, side QS = 10 cm. So, it's D. (last option)

Answer:

D

Step-by-step explanation:

I got it right on the test. 100%

Macy drove her car to visit her uncle. She came part of the way home after her visit. This graph shows the distance Macy was from her home during the course of the day. During which part of the graph is Macy visiting her uncle?

Answers

Answer:

part 11

Step-by-step explanation:

B

Step-by-step explanation:

hope that help!

Find the x-intercept of the graph of the linear equation y = 2x + 4.

Answers

Answer:

The x-intercept is -2

Step-by-step explanation:

PLEASE HELP!!!
Which of the following expressions is the prime factorization of 360?

A. 2 2 • 3 2 • 5
B. 2 4 • 3 • 5
C. 2 3 • 5 • 9
D. 2 3 • 3 2 • 5

Answers

Answer:

D. 2 3 • 3 2 • 5

Step-by-step explanation:

ig I need at least 20 characters to submit my answer. :)

Answer:

its d.

Step-by-step explanation:

Question: -3x – 10 = 32

Answers

Answer:

x = -14

Step-by-step explanation:

The first thing you are trying to do is get the x alone. so first you will look at 10 and do the opposite of the sign that you have. So you would take the -10 and make it +10. you would solve -10 + 10 and 32 + 10 because whatever you do to one side you do to the other. -10 +10= 0 and 32+10 = 42. Your equation now is -3x=42. we do not put -3x+0=42 because zero does not have a value. From here we would look at the -3x and do the opposite sign, which means dividing. whenever a number is next to x or any variable it is multiplication. For example, 7x is the same as 7*x. The opposite of multiplication is division. so we would do -3x/-3. We do 42/-3 because whatever we do to one side we do to the other. On the left side we are left with x then you add the equal sign and the quotient of 42/-3.

Answer: x = -14

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