Mathematics College

In an A.P. if Tₚ = q and Tq = p, then find the rth term.
Please solve this problem​

Answers

Answer 1

Formula:

We know that

nth term of the AP is Tn = a+(n-1)d

Where, a = First term

d = Common difference

n = number of terms

Now,

Given that

pth term of the A.P. = Tp = q

⇛a + (p-1)d = q

⇛(p-1)d = q - a

⇛d = (q-a)/(p-1) →→→→(i)

and

qth term of the A.P. = Tq = p

⇛a + (q-1) d = p

⇛ (q-1)d = p-a

⇛ d = (p-a)/(q-1) →→→→(ii)

From Eqn(i) and Eqn(ii)

⇛(q-a)/(p-1) = (p-a)/(q-1)

On applying cross multiplication then

⇛(q-a)×(q-1) = (p-a)×(p-1)

⇛q²-q-aq+a = p²-p-ap+a

⇛q²-q-aq = p²-p-ap

⇛ap-aq = p²-p+q-q²

⇛a(p-q) = (p²-q²)-(p-q)

⇛a(p-q) = (p+q)(p-q)-(p-q)

⇛ a(p-q) = (p-q){(p+q)-1}

On cancelling (p-q) both sides then

⇛a = (p+q-1) →→→→Eqn(iii)

On Substituting the value of a in Eqn(ii) then

⇛ d = [p-(p+q-1)]/(q-1)

⇛d = (p-p-q+1)/(q-1)

⇛d = (-q+1)/(q-1)

⇛d = -(q-1)/(q-1)

⇛d = -1

We have,

a = p+q-1 and d = -1

Now, rth term of the AP

⇛ Tr = a + (r-1)d

⇛Tr = (p+q-1)+(r-1)(-1)

⇛ Tr = p+q-1+(-r+1)

⇛ Tr = p+q-1-r+1

⇛ Tr = p+q-r

Therefore, Tr = p+q-r

Answer: rth term of the given A.P. is p+q-r

In An A.P. If T = Q And Tq = P, Then Find The Rth Term.Please Solve This Problem
Answer 2

Answer:

rth=q+p+qxp

Step-by-step explanation:

rth= 3 of the T and Tq added together and joined.

Related Questions

Determine the probability of the event.
A survey found that about 90% of the junior class is right handed. If 2 juniors are chosen at random out of
100 juniors, what is the probability that at least one of them is not right handed?
Give an exact answer as a decimal.

Answers

Answer:

The probability is 1/100

Step-by-step explanation:

This is because there are only ten left-handed juniors (on average). Therefore there isn't a great chance that you would end up with one.

Grapes are 2.55 per pound and on two separate occasions Dana went to the store to
buy grapes. The first time she went to the store she bought 3.25 pounds of grapes
and during the second visit to the store she purchase 1.25 pounds of grapes.
Rounded to the nearest cent, what is the total amount that Dana paid for the grapes?
$7.25
$12.35
$11.48
$7.05

Answers

Answer: $11.48

Step-by-step explanation:

First of all, you have to multiply 3.25 by 2.55 because the grapes are 2.55 per pound. That makes 8.2875 for the first occasion. Next, you have to multiply 1.25 by 2.55 for the second occasion. That makes 3.1875. You then have to add 8.2875 and 3.1875. You get 11.47500, and that rounded to the nearest cent is $11.48.

given the equation f(x)=-2x²+4x+6 find the average rate of change from x=1 and x=2​

Answers

Answer:

16

Step-by-step explanation:

1) Plug x=1 into equation

f(x) = -2(1)²+4(1)+6

f(x) = -2²+4+6

f(x) = 4+4+6

y = 14

(1,14)

2) Plug in x=2 into equation

f(x) = -2(2)²+4(2)+6

f(x) = -4²+8+6

f(x) = 16+8+6

y = 30

(2,30)

3) Use slope formula ([tex]\frac{y2-y1}{x2-x1}[/tex])

[tex]\frac{30-14}{2-1}[/tex]

[tex]\frac{16}{1}[/tex]

16

10. Which of the following is the best financial situation?

Answers

Answer:

Having enough to retire.

Step-by-step explanation:

The biggest long-term financial goal for most people is saving enough money to retire. The common rule of thumb that you should save 10% to 15% of every paycheck in a tax-advantaged retirement account like a 401(k) or 403(b), if you have access to one, or a traditional IRA or Roth IRA.

Suppose a worker makes $286.08 in one week. If he is paid $5.96 an hour for the first 36 hours he works and then $8.94 an hour in overtime pay for each additional hour, how many hours did he work overtime

Answers

Answer:

5.96 x 36 = 214.56.

286.08 - 214.56 = 71.52

71.52 divided by 8.94 = 8.

He worked 8 additional hours.

Answer:

The worker worked about 8 hours overtime.

Step-by-step

First we figure out how much they made without overtime.

Multiply 5.96 x 36 and you would get 214.56

Then we figure out how many hours he worked overtime

Multiply 8.94 times 8 and you would get 71.52

Then take 214.56 and add 71.52, you would get 286.08, the answer is 8 hours overtime.

There are 300 students in the 6th grade class. 252 of the students have received dragon
tickets. What is this as a percent?

Answers

The percentage of students in the 6th grade class that have received dragon  tickets is 84%.

Given the following data:

Total number of students = 300 studentsNumber of students with dragon tickets = 252 students

To determine the percentage of students in the 6th grade class that have received dragon  tickets:

A percentage is used to describe or represent a portion of a given population or total number of something.

Mathematically, the percentage for the given number of students is:

[tex]D = \frac{Students}{Total\;students} \times 100\\\\D = \frac{252}{300} \times 100\\\\D=0.84\times 100[/tex]

D = 84%

Read more on percentage here: https://brainly.com/question/14432715

When a number is divided by 5, it has a remainder of 4.
The number is between 35 and 40.
What is the number?

Answers

Answer:

37

Step-by-step explanation:

I plugged in the numbers between 35 and 40 and got this. No problem. :)

If you spend 3/5 of your $40 gift card, how much money will be left on it?

Answers

Answer:

$16

Step-by-step explanation:

1-⅗=⅖

40×⅖=16

Here's the answer

5x + y = 11
3x − y = 9

Answers

Answer:

x = 5/2y = -1.5

Step-by-step explanation:

5x + y = 11

        3x − y = 9

=> 5x + y = 11

           +3x − y = +9

=> 8x = 20

=> x = 20/8

=> x = 5/2

=> 5(5/2) + y = 11

=> 25/2 + y = 11

=> 12.5 + y = 11

=> y = 11 - 12.5

=> y = -1.5

Therefore, the answers are:

x = 5/2y = -1.5

Hoped this helped.

[tex]BrainaicUser1357[/tex]

Need help pls answer asap. Sorry the photo quality is bad.

Answers

Answer:

Step-by-step explanation:

1 + 3 = 4

so find the point 1/4 of the way from (-1, 2) to (7, 8)

x coordinate

Δx = ¼(7 - (-1)) = 2

x = x₀ + Δx

x = -1 + 2 = 1

y coordinate

Δy =  ¼(8 - 2) = 1½

y = y₀ + Δy

y = 2 + 1½ = 3½

(1, 3½)

What is the value of a on the triangle below?

Answers

Answer: answer 56 I’m the goat lol

Step-by-step explanation:

subtract 107 from 180 and you get 73 that’s one corner 73 +51 =124 and 180 - 124 = 56

in a survey of 500 voters 430 said they would vote for the same candidate again what percent of the votes would vote the same way again

Answers

86% would vote for the same person again

factorize completly Mn + np + or + rt​

Answers

Answer:

n (m + p) + r (o + t)

Step-by-step explanation:

You have to split the expression in half.

First, focus on mn + np, the common factor would be n.

So the first part of the answer would be mn ÷ n and np ÷ n.

Leading to it being n(m + p).

Then you focus on the second half or + rt.

You find the common factor, which is r.

You divide both sides by r.

Hence why you get r(o + t).

Lastly, you put them together, n(m + p) + r(o + t).

Hope this helps :)

Fill in the missing values.
151.5 cm =? m
151.5 cm = ? m
(Type an integer or a decimal.)

Answers

Answer:

151.5 cm = 1.515 m

151.5 cm = 1515/1000 m

What is the slope of the line. ?

Answers

Answer:

-1

Step-by-step explanation:

rise/run

rise=-1

run=1

-1/1=-1

send help send help send help

Answers

Answer:

B answer answer

[tex]the \: answer \: is \: b[/tex]

Tropical dried fruit costs $1.50 per pound and regular dried fruit costs $0.90 per pound. You want to create a mixed bag of tropical dried fruit and regular dried fruit that is worth $1.30 per pound. How many pounds of tropical dried fruit do you need if you have already purchased 50 pounds of regular dried fruit?

Answers

t = total amount of lbs of Tropical dried fruit

m = total amount of lbs of mixed bag

[tex]\begin{array}{lcccl} &\stackrel{fruit}{lbs}&\stackrel{per~lb}{price}&\stackrel{total}{price}\\ \cline{2-4}&\\ \textit{tropical fruit}&t&1.50&1.5t\\ \textit{regular fruit}&50&0.90&45\\ \cline{2-4}&\\ \textit{mix bag}&m&1.30&1.3m \end{array}~\hfill \begin{cases} t+50=m\\ 1.5t+45=1.3m \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 1st equation}}{1.5t+45=1.3\stackrel{m}{(t+50)}}\implies 1.5t+45=1.3t+65\implies 0.2t+45=65 \\\\\\ 0.2t=20\implies t=\cfrac{20}{0.2}\implies \boxed{t=100}[/tex]

Help me plzzzzzzzzzzzzz

Answers

Answer: It is D

Step-by-step explanation:

whats 5+5? please help quick quick quick

Answers

Answer:

It's 10 lol

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Because it is

Need help. Sorry if the pic quality is bad…

Answers

Your answer should be open circles between 10 and 12

A bakery sold a total of 500 cupcakes in a day, and 190 of them were vanilla flavored. What percentage of cupcakes sold that day were vanilla flavored?

Answers

Answer: 50/19

Step-by-step explanation:

I'm no math genius however I believe this is division.

500/190 gave me a fraction which is 50/19.

The awnser above me is not a percentage . The percentage of 19/50 would be 38%

If a cylinder has a volume of 648pi cm3( 3rd power) and a height of 8 cm, what is the radius?

Answers

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=\stackrel{cm^3}{648\pi }\\ h=8 \end{cases}\implies 648\pi =\pi r^2(8) \\\\\\ \cfrac{648\pi }{8\pi }=r^2\implies 81=r^2\implies \sqrt{81}=r\implies \boxed{9=r}[/tex]

how do i get more points? and why do i need it?

Answers

Answer:

You get more points by answering people's questions. You use points to get help from other people.

Answer: Answer people's questions to get points and use those points to get an answer to your question.

Please help!! Best answer gets brainliest<3

Answers

X= 25.65 + 16.5 - 12.45
X= 29.70

use the result (a+b)²=a²+2ab+b² to find the value of 49²+98+1


pls help me
I will give brainliest​

Answers

Answer:

2500

Step-by-step explanation:

a² + 2ab + b²

49² + 98 + 1

Comparing terms

a²= 49²

a= 49

2ab = 98

2× 49 × b = 98

98b = 98

b= 98/98

b = 1

or

b²= 1

b=√1

b= 1

a=49 and b= 1

Hence (a+b)²= (49+1)²

50²= 2500

through: (-5,1), parallel to y = -2/3x +2

Answers

Answer:

y = -2/3x-1

Step-by-step explanation:

The simplified equation after clearing the decimals is
-12.2 + 2.8w - 8.8 = 1.05w

Answers

Answer:

-21=-4w

w=5.25

but you don’t want decimals

so- you round down

w=5

Step-by-step explanation:

You combine like terms, and then make sure your variable is alone, the only way to get it alone from a ”mixed number”  is to divide

you do the same thing to both sides

so divde each side by -4

-21/-4 = 5.25

or with it rounded down since it’s under a five

It’s 5 with the decimals removed

i hope this helps

We figure 25 people will attend if it rains and 70 people will attend if it does not rain. The weather forecast indicates that there is a 20% chance of rain that day. What is the expected number of people who will attend the party?

Answers

Answer:

34

Step-by-step explanation:

20% of 70 + 80% of 25 = 14 + 20 = 34.

Answer:

61

Step-by-step explanation:

Assuming a linear relationship between the percent chance for rain and the number of attendees, the number is 20% of the way from 70 (0% chance) to 25 (100% chance).

The expected number of people with a 20% chance of rain would be 61.

(hope it helps)

The difference between two numbers is 8. if 2 is added to the bigger number the result will be three times the smaller number. Find the numbers.

Answers

Answer:

The bigger number is 13 and the smaller number is 5

Y=-6x-5

Please find the slope

Answers

Answer:

-6

Step-by-step explanation:

this is in y=mx+b form, where m is the slope ! so m is -6

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