The sum of the first 10 terms of a linear sequence is 5 and the sumof the next 10 terms is 215. Find the sequence.​

Answers

Answer 1

Answer:

The first term of the sequence is -8.95 with a common difference of 2.1.

The sequence is:

-8.95, -6.85, -4.75, -2.65...

Step-by-step explanation:

We are given that the sum of the first ten terms of a linear sequence is 5, and the sum of the next ten terms is 215.

And we want to find the sequence.

Recall that the sum of an A.P. is given by:

S = k / 2 ( a + xk)

Where a is the first term, k is the number of terms, and x_k is the last term.

We can represent our term values with the direct formula:

Xn = a + d (n-1)

Where the first term, x₁ = a.

The sum of the first ten terms is 5. Hence, S = 5, k = 10, a = x₁ and x_k = x₁₀:

(5) = 10/2 (a+xk)

5 = 5(a+(a+9d))

2a + 9d = 1

The sum of the next ten terms (that is, from x₁₁ to x₂₀) is 215. Hence, S = 215 when k = 10, a = x₁₁, and x_k = x₂₀:

(215) = (10)/2 (a + xk)

215 = 5((a+d(11-1))+(a+d(20-1)))

2a + 29d = 43

This yields a system of equations:

[tex]\left \{ {{2a+9d=1} \atop {2a+29d=43}} \right.[/tex]

Solve:

(2a + 9d) + (-2a - 29d) = (1) + (-43)

-20d = -42

d = 2.1

Consequently:

a = 1/2(1-9d)

= 1/2(1-9(2.1))

= -8.95

In conclusion, the first term of the sequence is -8.95 with a common difference of 2.1.

The sequence is:

-8.95, -6.85, -4.75, -2.65...  


Related Questions

Answer number 2 please.​

Answers

Answer:

Obtuse scalene triangle

Step-by-step explanation:

1. Angles:

-> Acute triangle: all angles less than 60° -> Right triangle: one angle is 90° -> Obtuse triangle: one angle is greater than 90°

- Given the information above, we can see that the triangle has one angle that's greater than 90° (129°), so this triangle is obtuse.

2. Sides:

-> Scalene triangle: all sides have different lengths-> Isosceles triangle: two sides have same length-> Equilateral triangle: all sides are the same

- Given the information above, we can see that all the sides in the triangle are different, so this triangle is scalene.

Therefore, the answer is an obtuse scalene triangle.

what is the pathgoren therem

Answers

a^2 + b^2=c^2 Pythagorean theorem the well-known geometric theorem the the sun of the square on the legs of a right triangle is equal to a square on the hypotenuse

A television weighs 50 pounds and a microwave
weighs 30 pounds. A TV occupies 4 cubic feet
and microwave occupies 3 cubic feet. A truck is
carrying 1500 pounds of cargo that occupies 138
cubic feet of space. Which system of equations
can be used to find the total number of
televisions, t, and microwaves, m, that are in the
truck?

Answers

Answer:

Step-50*t + 30*m = 1500,   (1)   (pounds)

4*t +  3*m = 138.    (2)   (cubic feet)

From (2), express 3m = 138 - 4t, and substitute it into (1). You will get

50t + 10*(138-4t) = 1500,  or

10t = 1500 - 1380  --->  10t = 1120  --->  t = 112 TVs.

From this point, find the number of microwaves on your own.

step by-step explanation:

Brooke has a savings account. The account balance is $550.87 at the beginning of the month. The list below shoes all of the activity for one month.

- a deposit of $75.98
- a withdrawal of $34.88
- a deposit of $84.12

What is the balance in Brooke's savings account at the end of the month?

Answers

Answer:

676.09

Step-by-step explanation:

550.87 + 75.98 = 626.85

626.85 - 34.88 = 591.97

591.97 + 84.12 = 676.09 therefore that's the amount at the end of the month

Reina's family is taking a road trip. Their car can travel no more than 304 miles without needing to refill the gas tank. They have traveled 221 miles since they last filled the gas tank. Reina knows that the inequality representing this situation is 221 + x < 304. Select from the drop-down menu to correctly interpret the solution of this inequality. Reina's family can drive ______ more miles before they need to refill the gas tank.​

Answers

Solving the inequality, it is found that the correct interpretation of the solution is:

Reina's family can drive 83 more miles before they need to refill the gas tank.​

The amount x of miles they can still travel is modeled by the following inequality:

[tex]221 + x \leq 304[/tex]

To solve it, we treat it similarly to an equality, hence:

[tex]x \leq 304 - 221[/tex]

[tex]x \leq 83[/tex]

Hence:

Reina's family can drive 83 more miles before they need to refill the gas tank.​

A similar problem is given at https://brainly.com/question/11713066

The answer prior to this is WRONG. The correct answer is "at most 83" miles.

Beth has 6 blue envelopes. She has 2 fewer yellow envelopes than blue envelopes. She has 7 times as many green envelopes as yellow envelopes. How many envelopes does Beth have in all?
PLEASE ANSWER MY LITTLE SISTER DOESN'T TRUST ME WITH THE REAL ANSWER PLSSSSSS

Answers

Answer:

38

Step-by-step explanation:

No. of yellow envelopes she has

= 6-2

= 4

No. of green envelopes she has

= 7×4

= 28

Total number of envelopes she has

= 6+4+28

= 38

A pancake recipe calls for 4 cups of flour and 3 cups of milk. Does a recipe calling for 2 cups of flour and 1.5 cups of milk use the same ratio of flour to milk?

Answers

Answer:

I think the answer is Yes

Step-by-step explanation:

For example, 2 cups of flour can equal 4 cups of flour by multiplying by two. So 1.5 cups of milk, you multiply by two and it is equivalent to 3 cups of milk. So in the end, it is equal and it's basically half of the pancake recipe. Hope it helps!

6 weeks to 12 days answer?

Answers

Are you looking for a ratio?

PARALLEL PERPENDICULAR OR NEITHER

Answers

Answer: maybe: perpendicular

Step-by-step explanation:

Parallel I think, hope this helps:)

Finding slopes. Please do as many questions as you can.

Answers

Answer:

Step-by-step explanation:

slope are hard tbh

Here are the slope answers to all of your questions!! :)

7. Slope is 1/2.

8. Slope is 2.

9. Slope is 1/2.

10. Slope is 26.

11. Slope is -5/6.

12. Slope is 16/13.

Hope this helps!! :)

Find the perimeter. Simplify your answer.

Answers

Answer:

Step-by-step explanation:

p = 10x + 2 + 7x - 6 + 8x

p = 25x - 4

Answer:

To Find the perimeter we add all the sides,

perimeter = 10x + 2 + 7x - 6 + 8x

= 25x - 4...ans

Step-by-step explanation:

Hope it Helps you!!

Help...Question 1 Objective: Apply properties of rhombi to solve mathematical and real-world problems. Rhombus LMNO is shown with its diagonals. Angle MNO measures 119º. What is the measure of angle LMN? M P N o​

Answers

Answer:

  61°

Step-by-step explanation:

As in all parallelograms, adjacent angles are supplementary.

  ∠LMN = 180° -∠MNO

  ∠LMN = 180° -119° = 61°

Pleeeeeeeeeeeeeeeeeaaaaaaaaaaaaaaaaase help

Answers

Answer:IT IS 170

Step-by-step explanation:

A cyclist travels 9.6 km in 30 minutes. What is his average speed in km/h?​

Answers

Answer:

[tex]\frac{95}{5} \frac{km}{hour}= 19.2 km/hour[/tex]

Step-by-step explanation:

Average speed = distance/time

Average speed = [tex]\frac{9.6}{30} \frac{km}{min}[/tex] ; multiply by 60min/1hour

Average speed = [tex]\frac{95}{5} \frac{km}{hour}= 19.2 km/hour[/tex]

p pennies added to 22 pennies

Answers

23 Pennie’s is the answer I believe

The hanger image below represents a balanced equation.
27
V
Find the value of v that makes the equation true.
U =
I need the answer

Answers

Answer:

2x =3

The hanger image given in the figure represents balanced equation.

Then we have to write an equation to represent the image.

In balanced form left side = right side

x + x = 1 + 1 + 1

2x = 3

The value v is 9.

What is equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that is a structure showing a balanced hanger we need to find the value,

So we can say since the hanger is balanced therefore the weight both sides will be equal,

Therefore,

v + v + v = 27

3v = 27

v = 27

Hence the value v is 9.

Learn more about equation click;

https://brainly.com/question/29657983

#SPJ2

Find the solution to the system of equations:

7x-8y=-23

7x-7y=-14

Answers

Answer:

Solutions: x = 7, y = 9;  or (7, 9)

Step-by-step explanation:

Given the following systems of linear equations:

7x - 8y = -23

7x - 7y = -14

Since the coefficients of x in the given system have the same sign, we could use the process of elimination by subtracting the two equations.

    7x - 8y = -23

-   7x - 7y = -14    

             -y = -9  

Divide both sides by -1 to solve for y:

[tex]\frac{-y}{-1} = \frac{-9}{-1}[/tex]

y = 9

Substitute the value of y into either one of the given equations to solve for x:

7x - 7y = -14

7x - 7(9) = -14

7x - 63 = -14

Add 63 to both sides:

7x - 63 + 63 = -14 + 63

7x = 49

Divide both sides by 7 to solve for x:

[tex]\frac{7x}{7} = \frac{49}{7}[/tex]

x = 7

Double-check whether x = 7 and y = 9 are valid solutions to the given system:

x = 7, y = 9:

7x - 8y = -23

7(7) - 8(9) = -23

49 - 72 = -23

-23 = -23 (True statement).

7x - 7y = -14

7(7) - 7(9) = -14

49 - 63 = -14

-14 = -14 (True statement).

Therefore, the solution to the given systems of linear equations are x = 7, and y = 9, or (7, 9).

A recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quarts of grape juice. How much of each ingredient would you need to make 100 quarts of punch?

Answers

Answer:

Step-by-step explanation:

Sparkling grape juice is made with 1.5 quarts sparkling water and 0.75 quarts grape juice. When these two get mixed we get 2.25 quarts sparkling grape juice

So for 2.25 quarts sparkling grape juice we require 1.5 quarts sparkling water

⇒ For 100 quarts sparkling grape juice we require  * 100 quarts of sparkling water

⇒ Sparkling water required for 100 quarts of sparking grape juice = 66.67 quarts

What is (-1/2) in mathematics

Answers

Answer: One half is the irreducible fraction resulting from dividing one by two (2) or the fraction ... One half often appears in mathematical equations, recipes, measurements

Step-by-step explanation: For example, if you wish to halve the fraction 5/7, write “* 2” beside the denominator “7.” There is no operation to perform to the numerator. Multiply the denominator by 2 to halve the fraction. Using the same example, 7 * 2 = 14. This means that half of 5/7 is 5/14.

What is the measurement of this angle?

Answers

Answer:

I believe it is 82.

Step-by-step explanation:

This is because a triangle's angles add up to 180. 180-65-33=82

Sorry if this is wrong

He gave the cashier $14.22 and received $2.63 in change. How much did the duffel bag cost?

Answers

Answer:

$11.59

Step-by-step explanation:

14.22-2.3=11.59

also this was like a question that gose "joe has 5 cookes, josie eats 3, how old is josie?"

PLSSSSS I REALLY NEED HELP IT IS DUE VERY SOON AND THIS IS MY LAST QUESTION I AM BEGGING EXTRA POINTS WILL BE INCLUDED FOR WHOEVER ANSWERS! GRAPH AND TABLE INCLUDED! the graph shows the relationship between the distance that a snail crawls and the time that it crawls. a. Use the points on the graph to make a table. b. Write the equation for the relationship and tell what each variable represents.

Answers

Answer: y=10x

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is y=1x+2

Which of the following represent opposites? –1 and 2 10 and 0 –20 and 21 11 and –11

Answers

Answer:

I am also indian i know this solution if you want to know commet here

what year was it, exactly 4 centuries before 1965?

Answers

Based on the number of years in a century, we can calculate that the 4 centuries before 1965 was 1565.

A century refers to a period of 100 years.

If we are looking for a period of 4 centuries therefore, this would be:

= 4 x 100

= 400 years

4 centuries before 1965 would therefore be:

= 1965 - 400

= 1565

In conclusion, the answer is 1565.

Find out more at https://brainly.com/question/17498856.

A used car is advertised for sale at "$300 down and $65 a month for 12 months. What is the total price of the car?​

Answers

Answer:

It will be 780

Step-by-step explanation:

explanation is that I multiply 65$ by 12

Find the perimeter. Simplify the answer

Answers

Answer:

10s-14

Step-by-step explanation:

Perimeter of rectangle = 2s+2(4s-7)

                                      = 2s+8s-14

                                      = 10s-14

= > Perimeter of rectangle = 2(l + b)

= > 2(s + 4s - 7)

= > 2(5s - 7)

= > 10s - 14...ans

Step-by-step explanation:

Hope it Helps you!!

PLEASE HELP I NEED HELP

Which verb of ser do I use?

Example: son, sois, somos, es, eres, soy

Ricardo y yo _____.

I WILL GIVE BRAINLIEST

Answers

Answer: Ricardo y yo somos

Answer:

somos

Step-by-step explanation:

somos means us

Ricardo and us

The interval (-1, 1) is best described as

Answers

Answer: There's an increasing interval between -1 and 1

While x goes from -1 to 1, the value of y increases (from -2 to 2).

How many solutions are there to the equation below?
5x + 15 = 5(x+4)

Answers

Answer:

I think it 2 solution to the problem you can add or multiple

What is the distance between −93 and 114 on a number line?

Answers

Answer:

207

Step-by-step explanation:

By counting the amount of numbers to get from -93 to 114, you count a total of 207. This means it takes 207 steps to get from -93 to 114.

When finding the distance between negative and positive numbers you can also add the numbers together to get the total distance between the numbers.

Answer: what ever u said on the answer to one of my questions got deleted lol

Step-by-step explanation:

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