The sum of 8th term of an A.P is 160 while to sum of the 20th term is 880. Find the 43rd term​

Answers

Answer 1
Let a and d be the first term and common difference, respectively. Then

the 8th term is a+7d
the 20th term is a+19d

The sum of the first 8 terms is
(a)+(a+d)+(a+2d)+...+(a+7d) = 8a+28d

The sum of the first 20 terms is
(a)+(a+d)+(a+2d)+...+(a+19d) = 20a+190d

So

8a + 28d = 160
20a+ 190d = 880

40a + 140d = 800
40a + 380d = 1760
240d = 960
d = 4

8a + 112 = 160
8a=48
a =
6

The first term is 6 and the common difference is 4.

The 43rd term is a+42d = 6+42(4) = 6+168 = 174

The sum of the first 12 terms is
(a)+(a+d)+(a+2d)+...+(a+11d) = 12a+66d = 12(6)+66(4) = 72+264 = 336
Answer 2

The value of the 43rd term of the arithmetic sequence will be 482.

What is the sum of an arithmetic sequence?

Let a be the first term, L be the last term, n be the number of terms, and d be a common difference.

Then the sum of the arithmetic sequence will be

Sₙ = (n / 2)[a + L]

Sₙ = (n/2) [2a + (n − 1) d]

An A.P.'s eighth term is worth 160 while their twentieth term is worth 880.

160 = (8/2)(2a + 7d)

2a + 7d = 40                        ...1

880 = (20/2)(2a + 19d)

2a + 19d = 88                       ...2

From equations 1 and 2,

40 - 7d + 19d = 88

12d = 48

d = 4

Then the value of 'a' is given as,

2a + 7(12) = 40

2a = 40 - 84

2a = -44

a = -22

The value of the 43rd term is given as,

aₙ = a + (n - 1)d

a₄₃ = - 22 + (43 - 1)(12)

a₄₃ = - 22 + 42 x 12

a₄₃ = - 22 + 504

a₄₃ = 482

More about the sum of arithmetic sequence link is given below.

https://brainly.com/question/25749583

#SPJ5


Related Questions

Insert 5 geometric means between -4 and -62 500​

Answers

9514 1404 393

Answer:

  Either of ...

{-20, -100, -500, -2500, -12500}{20, -100, 500, -2500, 12500}

Step-by-step explanation:

For some common ratio r, the first of the "geometric means" will be -4r, the next will be -4r^2, and so on. The 5th will be -4r^5, and finally, -62500 will be -4r^6.

Solving this last relation for r gives ...

  -4r^6 = -62500

  r^6 = 15625

Then r can be either of ...

  r = ±15625^(1/6) = ±5

For r = 5, the means are ...

  -4·5 = -20, and -100, -500, -2500, -12500

For r = -5, the means are ...

  -4(-5) = 20, and -100, 500, -2500, 12500

Quis
bentuk pangkat dari
2² + 3² - 2²=
note:. user Indonesia​

Answers

Answer:

9 Should be your answer

Step-by-step explanation:

[tex]2^{2}[/tex] = 4

[tex]3^{2}[/tex] = 9

These will help us as we solve this problem.

Then: 2² + 3² - 2²

= 4 + 9 - 4

= 9

Kind requests:

Please give brainliest :D

[tex]\sf 7-5x=-43[/tex]

Answers

Answer:

[tex]\sf\longmapsto \: x = 10[/tex]

Step-by-step explanation:

Subtract 7 from both sides:

7−5x−7=−43−7

Simplify:

−5x=−50

Divide both sides by −5:

[tex]\sf\longmapsto \: \frac{ - 5x}{ - 5} = \frac{ - 50}{5} [/tex]

[tex]\sf\longmapsto \: x = 10[/tex]

[tex]\boxed{\sf Answered \: By\: Subhash} [/tex]

[tex]\boxed{\sf Answered \: By\: Subhash} [/tex]

[tex]\boxed{\sf Good\: luck \: for \: your \:assignment} [/tex]

Answer:

x=10

Step-by-step explanation:

[tex]7-5x=-43[/tex]

[tex]7-5x-7=-43-7[/tex] Subtract

[tex]-5x=-50[/tex]

[tex]\cfrac{-5x}{-5}=\cfrac{-50}{-5}[/tex] Divide

[tex]x=10[/tex]

Determine if the following are true or false statements.

- If it is below 32° outside, then it is snowing. T or F

- If m∠2=25°, then it is an acute angle. T or F

- If two angles are supplementary, then they add up to 180°. T or F

- If two angles are complementary, then they are both 45° T or F

Answers

Answer:

1. T

2. T

3. T

4. F

Step-by-step explanation:

1. The tempature must be 0 degrees celcus or 32 degrees fahrenheit or below to snow.

2. An acute angle is less than 90 degrees

3. Supplementary angles are 2 angles that add up to 180.

4. Complementary angles are any 2 angles that add up to 90 degrees BUT they do not have to be only 45 degrees and can be any 2 degrees that add up to 90.

Please help me solve this

Answers

Answer:

9

Step-by-step explanation:

2(m+2) = 22

Using the distributive property, you can multiply the 2 to both the "m" term and the "2".

2m + 2*2 = 22

2m + 4 = 22

Then you isolate the variable and solve.

2m = 22 - 4

2m = 18

m = 9

2(m + 2) = 22

2(m) + 2(2) = 22

2m + 4 = 22

2m = 22 - 4

2m = 18

2m / 2 = 18 / 2

m = 9

To distribute the 2 to each term inside the parentheses means to multiply the 2 by both terms in the parentheses so

2(m + 2) means (2 × m) + (2 × 4)

A sample of gold has a mass of 579 g. The volume of the sample is 30 cm3. What is the density of the gold sample?

Answers

The density of the gold sample is 19.3g/cm³

Let the mass of the gold sample be represented by m

m = 579 g

Let the volume of the gold sample be represented by V

V = 30 cm³

Let the density of the gold sample be represented by ρ

The formula for the density is:

[tex]Density = \frac{Mass}{Volume}[/tex]

[tex]\rho = \frac{m}{V} \\\rho = \frac{579}{30} \\\rho = 19.3 g/cm^3[/tex]

The density of the gold sample is 19.3g/cm³

Learn more here: https://brainly.com/question/17780219

Hi- So this is a simple question that I keep forgetting how to answer! HELPPPP

Ok so, The scale factor from Triangle A to Triangle B is 2, so Triangle B is 2 times bigger than Triangle A.
How much bigger is the area of Triangle B than the area of Triangle A?

HELPPPP

Answers

Answer:

4 times bigger

Step-by-step explanation:

1. The area of an object dilated by a scale factor (SF) will be equal to (SF)^2.

2. For example, let's say the base and height of Triangle A is 4 and 8. The area would be 16 units squared. The base and height of Triangle B would be 8 and 16. The area would be 64 units squared.

3. As you can see from the aforementioned example, the SF (2) was squared  and then multiplied by 16 to get 64.

Therefore, Triangle B's area is 4 times bigger than Triangle A's area.

Lillian's bedroom door is 9 feet tall and 3 feet wide. A new door would cost $3.00 per square foot. How much would a new bedroom door cost in total?

Answers

Answer:

$81.00

Step-by-step explanation:

First find the square feet:

9*3= 27

Then find total cost:

27*3= 81

Hope this helps! :)

Find the point if intersection of these two lines using algebra.Y= -x+3 and y=3x+2

Answers

Answer:

x = 1/4, y = 11/4

Step-by-step explanation:

hope this helps

50 POINTS!
PLEASE HELP THIS MAKES NO SENSE AT ALL!! IM BEING TIMED

Answers

Answer: the last one i think if i'm wrong then im so sorry

Find the value of K given x=4 and y=16?

Answers

Answer:

When y = 20 ,x is −5

Step-by-step explanation:

Which type of parent function is f(x) =^3cubed x

A. Square root
O B. Cube root
O C. Reciprocal
D. Quadratic
Help quick!!!

Answers

Answer:

Cube Root

Step-by-step explanation:

Because there is a 3 outside the symbol.

That means the equation is stating: y * y * y = x

Hope this helps :)

write the equation of the line perpendicular to the given line y= -2/3 x + 1

Answers

since the equation of the line passing through the given point is perpendicular to the given line(m2= -1/m1)

using the formula y=mx+c

y=2/3x +1

m1=2/3

m2= -1/2/3

m2= -3/2

the slope of the second line is -3/2 and it passes through the point(3,-2)

using the formula y-y1 = m(x-x1)

y-(-2)= -3/2(x-3)

y+2= -3/2(x-3)

multiply both sides by 2

2(y+2) = -3(x-3)

2y+4 = -3x+9

2y = -3x+5

y= -3/2x + 5/2

How do I solve 5x - 4x^2

Answers

Answer:

If you are asking,

5x - 4x^2=0

x(5-4x)=0

Either,

x=0

or,

5-4x=0

x=5/4

If factor,

5x - 4x^2

x(5-4x)

If difference,

5x - 4x^2

The same as they are not like terms.

DO NOT ANSWER IF YOU DO NOT KNOW


What is 1 way you can tell if two people are paying the same rate?

Answers

Answer:

By saying "paying the same rate"

I believe you want to know for example when two people are buying a product how to know if they are paying the same amount.

If so then there are a couple of factors at play.

First of all you need to identify the GDP of the product and the amount of tax/VAT which if calculated properly may help you tell if they are paying the same amount or not.

can someone help me ??

Answers

Answer:

x=5

Step-by-step explanation:

Brainliest?PLEASE?

Answer: x=-5

I hop that helped I would appreciate brainliest if possible :)

Brandon enters bike races 8 1/2 miles every 1/2 hour.

Answers

i have no idea what it is

A line segment is defined by which of the following statements?
А Two rays that share a common endpoint.
B.
The set of all points that are a fixed distance from a given point.
С
All points between and including two given points.
D
A straight path connecting two points and extending infinitely in both directions.

Answers

The only given option that correctly defines a line segment is;

Option C; All points between and including two given points.

      In geometry in mathematics, a line segment is defined as a part of a line that is bounded by two distinct end points.

Now, let us look at the options;

Option A; This is not correct because a line segment must have 2 distinct endpoints

Option B; This is not correct because a line segment is a part of a line and not a set of points.

Option C; This is correct because it tallies with our definition of line segment.

Option D; This is not correct because a line segment does not extend infinitely.

Read more at; https://brainly.com/question/18089782

PLEASE HELP I WILL GIVE YOU BRAINLIEST ANSWR!!!!!!

Answers

Answer:

Domain: (- infinity, infinity) Range: (-infinity, infinity)

Step-by-step explanation:

ok. look at the x axis.. the graph goes on forever... now y axis, it continues so both are infinity.

The perimeter of a rectangle is 84 cm. If the length is 17 cm, how wide is the rectangle?
A) First write an equation you can use to answer this question. Use w as your variable in the equation

B) Solve your equation in part [A] to find the width of the rectangle.
Answer: The rectangle is
cm wide.

PLS HELP I NEED THIS ASAP

Answers

Answer:

width = 25cm

Step-by-step explanation:

perimeter = 84

length =17

A) 84 = 17(2) + 2w

B) 84 = 34 + 2w

 -34      -34

50=2w

/2     /2

25=w


What is the measure of the
third angle of this triangle?

Answers

Answer:

20 degrees

Step-by-step explanation:

180-120-40=20

HELP PLEASE!!
Write a recursive rule for an=1/3•4^n-1

A.) an=1/3•an-1
B.) an=4•1/3an-1
C.) an=1/3•4an-1
D.) an=4•an-1

Answers

Answer:

D.) an = 4 * an-1

Step-by-step explanation:

a(n) = (1/3) * 4^(n-1)

a(n-1) = (1/3) * 4^(n-1-1) = (1/3) * 4^(n-2)

Thus,

a(n) = (1/3) * 4 * 4^(n-2) = 4 * [(1/3) * 4^(n-2)] = 4 * a(n-1), so that

a(n) = 4 * a(n-1).

The total height of three people is 14 ft. Person A is 1 ft taller than Person B. Person C is 2 feet shorter than Person B. How tall is person A?

A. 6ft
B. 3ft
C. 5ft
D. 4ft​

Answers

Step-by-step explanation:

A+B+C = 14

B+1 +B + B-2 = 14

3B -1 = 14

3B = 14+1

3B =15

B = 5

Therefore, A = 5+1 = 6 ft (option A)

>> Answer

__________

[tex] \: [/tex]

14 = A + B + C

14 = (B + 1) + B + (B - 2)

14 = 3b - 1

14 + 1 = 3b

15 = 3b

b = 15 ÷ 3

b = 5

.

A = B + 1

A = 5 + 1

A = 6 (A.)

Tan^2 0+Tan^2 30+Tan^2 60+Sin^2 0​

Answers

Answer:

2.996519411885697

Step-by-step explanation:

[tex] \tan(20) + \tan(230) + \tan(260) + \sin(20) = 2.996519411885697[/tex]

mark me brainliest

What force would have been applied to the bus from t=16 s to t=21 s? Assume the mass of the bus was 50 kg.

Answers

Applying Newton's Second Law, it is found that the force, in Newtons, is given by:

[tex]F = 10[v(21) - v(16)][/tex]

Newton's Second Law states that Force, in Newtons, is mass times acceleration, that is:

[tex]F = ma[/tex]

In this problem, mass of 50 kg, thus [tex]m = 50[/tex]

Acceleration is change in velocity divided by change in time, that is:

[tex]a = \frac{\Delta_v}{\Delta_t}[/tex]

In this problem, we don't know the velocities, but know that time is from 16s to 21s, thus:

[tex]\Delta_t = 21 - 16 = 5[/tex]

[tex]\Delta_v = v(21) - v(16)[/tex]

Thus, the force is given by:

[tex]F = ma[/tex]

[tex]F = m\frac{\Delta_v}{\Delta_t}[/tex]

[tex]F = 50\frac{[v(21) - v(16)]}{5}[/tex]

[tex]F = 10[v(21) - v(16)][/tex]

A similar problem is given at https://brainly.com/question/18801986

In ΔDEF, EF = 15, FD = 13, and DE = 4. Which list has the angles of ΔDEF in order from smallest to largest?

Answers

Answer:

< F , < E, < D

Step-by-step explanation:

ΔDEF

Arrange the sides from smallest to largest

DE = 4, FD = 13, and EF = 15.

Largest side opposes the largest angle, medium side opposes the medium angle, smallest side opposes  the smallest angle.

the angles of ΔDEF in order from smallest to largest

< F , < E, < D

8z + 6 = 7z + 4
I need help with it please show the steps

Answers

z=2 thats the answer to your problem

PLS HELP ASAP ILL GIVE BRAINLIEST TYSM

Answers

Answer:

3x+2=16

Step-by-step explanation:

Answer:

the answer is most likely to be rather the first or second choice, but i choose B

Step-by-step explanation:

*Hope this helps*

based on what i understood, 3 green rectangles (or whaever that shape is), the 2 red squares, and the 16 small yellow squares. and the answer choices have

3x - 2 = 16

3x +2 = 16

3x + 4 = 20

3x = 24

and i dont think its 3x + 4 = 20 or 3x = 24 because there isn't any shapes to represent the 4, 20, and 24.

I might be wrong but i hope its right...

just give me the coordinates plzplzplz

Answers

Answer:

(0,4) and (5,-3)

Step-by-step explanation:

7) The sum of the angle measures of a
quadrilateral is 360°. Find the value of x.
24
2

Answers

Answer:

x=120°

Step-by-step explanation:

X+X+1/2X+1/2X=360

combine all like variables

X+X=2X

1/2X+1/2X=X

2X+X=3X

3X=360

isolate x by dividing both sides by 3

360÷3=120

X=120

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