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.

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Related Questions

Given m||n, find the value of x.
т
Rt
>m
(2X-22)
(5x-8)°
>

Answers

Given angles are supplementary.

[tex]\\ \sf\longmapsto 2x-22+5x-8=180[/tex]

[tex]\\ \sf\longmapsto 7x-30=180[/tex]

[tex]\\ \sf\longmapsto 7x=180+30=210[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{210}{7}[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

your friend says that there are 36 feet in 12 yards is your friend correct? explain your reasoning.

PLEASE HURRY!!​

Answers

Answer:

Yes

Step-by-step explanation:

1 yard is 3 feet. so 12 yards is 36 by 12*3

i realy need it very desparate

Answers

Answer: how to stop deppreshon

Step-by-step explanation: The mainstay of treatment is usually medication, talk therapy, or a combination of the two. Increasingly, research suggests these treatments may normalize brain changes associated with depression.

Please help me this question…

Answers

the area of the rectangle is 0.1 square meter

Area of rectangle is Length * width

Let's solve the equations
It's clear from the rectangle that the widths are equal.
So 2x-1=x+2
2x-x=2+1
X=3 cm

Let's find y from the heights
2y=3y-1
3y-2y=1
y=1cm

Let's apply the area formula
A= L*W
3*1
= 3 cm ^2

We know 1 meter =100 cm

So 3cm * 1m^2/(100cm )^2
Area in meter = 0.0003 meter^2


Reasoning There were 43 students on the playground. Some more students joined them. Now there are 63 students on the playground. How many students joined? EnVision Lesson 3-5

Answers

Answer:

20

Step-by-step explanation:

63 - 43 = 20

Answer:

20 students

Step-by-step explanation:

because 43+s=63

63-43=20

s=20

so it have 20 students on the playground

The picture needs to be answered.

Answers

Answer:

if 3 children go to the water park, 4 adults can go: TRUE

if 6 children go to the water park 3 adjults can go: FALSE

no adults, 6 children: TRUE (even 9 children can go)

no children, 6 adults: TRUE

10x is indeed the cost of the children

15y is indeed the cost of the adults

Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of
lemonade they sell.
Write an equation that shows how their total earnings, y, depend on the number of cups sold,
X.
Do not include dollar signs in the equation.
y =

Answers

Answer:

y= x • 2

Step-by-step explanation:

The amount of money they make is dependent of how many 2 dollar cups they sell.

(please crown me brainleist I need to level up)

Peter brought 8 lemons for 6 dollars each lemon was the same price what was the cost for 1 lemon.

Answers

Answer:

75 cents

Step-by-step explanation:

We can use a ratio to solve

8 lemons      1 lemon

------------- = ------------

6 dollars        x dollars

Using cross products

8x = 6*1

8x = 6

Divide by 8

8x/8 = 6/8

x = .75

One lemon costs .75

the square root of negative 9 is not negative 3 because..​

Answers

Answer:

You cant have a negative square root

Explanation:

The answers will always be positive or a perfect square

Hope this Helps

Find the value of 4+n when n=12

Answers

Answer:

16

Step-by-step explanation:

N equals 12, so

4 + 12 = 16

Answer:

4 + n = 16

Step-by-step explanation:

n = 12 so 4 + 12 is 16

Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.

Answers

Basically, it is not a function because 1 domain (in this case, 5) can not be connected to two different ranges(1 and -2). Each domain must only connect to one range.

Given m|n, find the value of x. (6x-9) → (5x+10) ​

Answers

>> Answer

__________

[tex] \: [/tex]

6x - 9 = 5x + 10

6x - 5x = 10 + 9

x = 19

An engineer is estimating the weight of a steel beam. The actual weight of the beam is 152 pounds. The engineer's estimate is 150 pounds.
Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers to the nearest tenth.

Answers

Answer/Step-by-step explanation:

To find the absolute difference, we simply have to see by how much pounds the estimation was off.

The real measure was 152 pounds, the estimated weight was 150.

D = 152- 150 = 2 pounds.

For the percent of error, we divide the absolute difference (52) by the real value () and we'll get the % of error.  So,

%D = 52 / 152 = 0.0034, so 0.34%  

A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence of three actions. Each action consists of either pressing one of the buttons or pressing a pair of them simultaneously.

Answers

There are several ways the door can be locked, these ways illustrate combination.

There are 3375 possible combinations

From the question, we have:

[tex]\mathbf{n = 5}[/tex] --- the number of digits

[tex]\mathbf{r = 3}[/tex] ---- the number of actions

Each of the three actions can either be:

Pressing one buttonPressing a pair of buttons

The number of ways of pressing a button is:

[tex]\mathbf{n_1 = ^5C_1}[/tex]

Apply combination formula

[tex]\mathbf{n_1 = \frac{5!}{(5-1)!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5!}{4!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5 \times 4!}{4! \times 1}}[/tex]

[tex]\mathbf{n_1 = 5}[/tex]

The number of ways of pressing a pair is:

[tex]\mathbf{n_2 = ^5C_2}[/tex]

Apply combination formula

[tex]\mathbf{n_2 = \frac{5!}{(5-2)!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5!}{3!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5 \times 4 \times 3!}{3! \times 2 \times 1}}[/tex]

[tex]\mathbf{n_2 = 10}[/tex]

So, the number of ways of performing one action is:

[tex]\mathbf{n =n_1 + n_2}[/tex]

[tex]\mathbf{n =5 + 10}[/tex]

[tex]\mathbf{n =15}[/tex]

For the three actions, the number of ways is:

[tex]\mathbf{Action = n^3}[/tex]

[tex]\mathbf{Action = 15^3}[/tex]

[tex]\mathbf{Action = 3375}[/tex]

Hence, there are 3375 possible combinations

Read more about permutation and combination at:

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how do i find the sum of (5/4q + 1) + (q - 4) + (-1/4q + 2)

Answers

Answer:

2q-1

Step-by-step explanation:

Add:

Look at only the q's inside the parenthesis and see if there are other q's in it, in this case there are none.

Now look outside the parenthesis and add the q's outside of it which is 5/4q, q and -1/4q

5/4q-1/4q is q

q+q is 2q

Now do the same thing with the numbers that doesn't have variables

1-4+2=-1

So the answer is 2q-1

Hope this helps!

Answer:

2q -1

Step-by-step explanation:

(5/4q + 1) + (q - 4) + (-1/4q + 2)

5/4q + 1 + q - 4 - 1/4q + 2

5/4q + q - 1/4q + 1 - 4 + 2

2q -1

How many 1/4 cup servings are in 5/6 cups of yogurt?​

Answers

Answer:

3.3

Step-by-step explanation:

1/4*3 = 3/12 (find lcd lowest common factor )

5/6 *2 10/12 figure out how many time 3 goes into 10 about 3.3 repeating

Answer:       [tex]\right] \left[\begin{array}{ccc}0.3 cups\\\end{array}\right] \\[/tex]

Step 1: Write the problem as a mathematical expression.

1/4 and 5/6

Step 2: Convert the fraction to a decimal by dividing the numerator by the denominator.

0.3 cups

Definitions:

A. Fraction- A number used to name a part of a group or a whole. The number below the division line is the denominator, and the number above the division line is the numerator.

B. Expression- A mathematical symbol, or combination of symbols, representing a value, or relation.

Have a great day!

Madelyn has two summer jobs. During the week she works in the grocery store, and on the weekend she works at a nursery. She gets paid $22 per hour to work at the grocery store and $21 per hour to work at the nursery. How much does she earn if she works 11 hours at the grocery store and 10 hours at the nursery? How much does she earn if she works gg hours at the grocery store and nn hours at the nursery?

Answers

Answer:

242$ in grocery store and 210$ in nursery

Step-by-step explanation:

To make rice in a factory, Lois mixes rice and water in the ratio 2 : 3. If she uses 10 cups of rice, how many
cups of water does she need?

Answers

Answer:

15 cups

Step-by-step explanation:

2:3

10:?

2x5:3x5

10:15

I need the answer for this

Answers

Answer:

JK = 12.6

Step-by-step explanation:

Similarity says ratio of any cooresponding sides are equal to the ratio of any other cooresponding sides. SO

25.2/66 = JK/33

33(25.2/66) = JK

12.6 = JK

Work out the size of angle x 126 degrees exterior and 43 degrees interior

Answers

Answer:

The answer is 83°

Step-by-step explanation:

by the sum of iner and outer angle=180°

180-126= 54°

x=180-43+54

x=180-97

x=83°

hope that helped.?<3

how do I do this please help

Answers

Answer:

i do not know what it all says

Step-by-step explanation:

Explain why it does not matter which point you choose when writing the
equation of the line in point-slope form, given two points.

Answers

Answer:

because, it will completely change the slope

Step-by-step explanation:

It does not matter which point you choose when writing the

equation of the line in point-slope form because the slope of the line remains same.

What is a slope ?

A slope can be thought of as rate of change of y axis with respect to x axis.

We have been asked in this statement that why it doesn't matter that which point we choose when writing the equation in point slope form.

Let us understand this with an example,Suppose we have two pair of points. (x₁,y₁) = (2,3) and (x₂,y₂) = (5,9).

We know slope(m) is = (y₂-y₁)/(x₂-x₁).

Slope(m₁) = (9-3)/(5-2)

               = 6/3

               = 2.

Now if interchange the points  (x₁,y₁) =  (5,9) and  (x₂,y₂) =  (2,3).

Slope(m₂) = (3-9)/(2-5)

                = -6/-3

                = 2.

So, even when interchanging the points the slope m₁ = m₂ this is the reason why it doesn't matter which point we choose.

learn more about slope here :

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1) Jen spends $5.98 on ribbon. Ribbon costs $0.92 per meter. How many
meters of ribbon does Jen buy?

Answers

Answer:

6.5

Step-by-step explanation:

5.98÷0.92= 6.5m

Write an equation. A number is doubled, then 9 is added. The result is 23.

Answers

Answer:

2n + 9 = 23

Step-by-step explanation:

let the number be n then double the number is 2n and adding 9 gives

2n + 9 ( the result is 23 ) , so

2n + 9 = 23 ← is the equation modelling the statement

Given that f ( x ) = 3 x − 7 and g ( x ) = 3 x + 9 , evaluate f ( g ( 2 ) )

Answers

Answer:

38

Step-by-step explanation:

f ( x ) = 3 x − 7

g ( x ) = 3 x + 9

f(g(2))

First find g(2)

g(2) = 3(2)+9 = 6+9 = 15

Then find f(15)

f(15) = 3*15 -7 = 45 -7 =38

find the slope with the given numbers​

Answers

Answer:

[tex]m=-\frac{1}{26}[/tex]

Step-by-step explanation:

Formula:

[tex]Slope:m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]

----------------------------------------------------------------------------------------------------------------

Work:

[tex]m=\frac{-15-(-16)}{-7-19}\\\\m=-\frac{1}{26}[/tex]

Ben deposited $500 into a savings account at a local bank that earned 5% interest per
year. How much interest does he earn per year?

Answers

Answer:

$25

Step-by-step explanation:

500*0.05=25

Answer:

$25 because 100 is half of 500

{x: x belongs to N and (x-1)(x-2) = 0}, finite set or infinite set?

Answers

Answer: Finite Set

Explanation:

We have a set of x values such that (x-1)(x-2) = 0. Breaking that down leads to either x-1 = 0 or x-2 = 0 through the zero product property. Solving each of those equations gets us x = 1 and x = 2 as the two items in this set.

So the original set your teacher gave you turns into the roster form {1,2}. There are two items in this set and we can see it's a finite set since it does not go on forever. Note that everything in this set is a natural number.

{(2, 2),(4, 4),(6, 6),(8, 8)}
Is a Function – { ( 2, 2 ),( 4, 4 ),( 6, 6 ),( 8, 8 ) }
Is not a Function – { ( 2, 2 ),( 4, 4 ),( 6, 6 ),( 8, 8 ) }

{(0, 3),(3, 5),(5, 6),(8, 4)}
Is a Function – { ( 0, 3 ),( 3, 5 ),( 5, 6 ),( 8, 4 ) }
Is not a Function – { ( 0, 3 ),( 3, 5 ),( 5, 6 ),( 8, 4 ) }

{(1, 2),(3, 3),(4, 8),(6, 3)}
Is a Function – { ( 1, 2 ),( 3, 3 ),( 4, 8 ),( 6, 3 ) }
Is not a Function – { ( 1, 2 ),( 3, 3 ),( 4, 8 ),( 6, 3 ) }

{(3, 4),(5, 2),(5, 6),(7, 3)}
Is a Function – { ( 3, 4 ),( 5, 2 ),( 5, 6 ),( 7, 3 ) }
Is not a Function – { ( 3, 4 ),( 5, 2 ),( 5, 6 ),( 7, 3 ) }


which is not a function and which is a function?

Answers

{(2, 2),(4, 4),(6, 6),(8, 8)} Is a function.

{(0, 3),(3, 5),(5, 6),(8, 4)} Is a function.

{(1, 2),(3, 3),(4, 8),(6, 3)} Is a function.

{(3, 4),(5, 2),(5, 6),(7, 3)} Is not a function.

For a relation to be a function, every x value must have only one y value.

Given the function f(x)=x^2+2x+1, find each value of the function

Answers

Answer:

1 9/16

Step-by-step explanation:

F(1/4) means u plug in 1/4 for x

so the equation would be

f(1/4)=1/4^2+2 1/4 + 1

f(1/4)=1/16+1/2+1

f(1/4)= 9/16 +1

f(1/4)= 1 9/16

its not nine teen its one and 9 over 16 just clarification

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