In an A.P. if Tₚ = q and Tq = p, then find the rth term.
Please solve this problem
Answers
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
Answer:
rth=q+p+qxp
Step-by-step explanation:
rth= 3 of the T and Tq added together and joined.
Related Questions
a storage tank is 60% filled with chemical solution. The storage tank holds 1,280 liters of chemical solution. How many liters of chemical solution are needed to fill the storage tank to the top?
Answers
Answer:
Step-by-step explanation:
write a proportion and cross multiply to solve for x
[tex]\frac{60}{100} = \frac{x}{1280}[/tex]
100x=76,800
x=768
60% full is 768 L. If the tank can hold 1,280 Liters, you need 512 more to fill it.
Alternatively...if the tank is 60% full, we need 40% more to fill it
[tex]\frac{40}{100} =\frac{x}{1280}[/tex]
100x=51,200
x=512 L
Two tanks hold a total of 61 gallons of a toxic solvent. One tank holds 4 gallons more than twice the amount in the other. How many gallons does each tank hold?
Answers
Answer:
tank 1 : 19 gallons
tank 2 : 42 gallons
Step-by-step explanation:
tank 1 : x
tank 2 : 2x+4 ( 4 more than twice the other )
x + ( 2x + 4 ) = 61
3x + 4 = 61 [ add x + 2x = 3x ]
3x = 57 [ subtract 4 on both sides ]
x = 19 [divide 3 on both sides ]
tank 1 : 19 gallons
tank 2 : 42 gallons
The large rectangle below represents one whole. What percent is represented by the shaded area? %
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Answer:
Step-by-step explanation:
would help a lot if you show the picture or describe it very well.
What is the answer to the following question?
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SAS similarity
Step-by-step explanation:
You have two side ratios and the angle between the sides with those ratios. The appropriate similarity theorem is SAS.
Find the circumference of a circle with a radius of 8 mm.
Answers
Answer:
C=50.27mm
Step-by-step explanation:
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is (33,10), (35,8), and (36,10) a function
Answers
Answer: yes it’s a function because the x values aren’t repeating
1
Renee is comparing prices from Kay's Catering and Weddings 'R' Us to serve the meals for her wedding
dinner. The catering cost, c, for each catering service Renee is considering, based on x meals served, is
shown on the coordinate grid.
Catering Cost for Wedding
2000
1800
1600
Kay's Catering
A
1400
1200
1000
C= 10m + 800
C = 15m + 400
Catering Cost ($)
800
Weddings 'R' US
B
C =
600
5m + 800
am + 800
400
200
C=
10 20 30 40 50 60 70 80 90 100
Number of Meals
с
C= 800m + 10
C = 400m + 15
Which system of equations is best represented by this graph?
D
C = 3m + 1,600
C =
M + 80
Answers
Answer:
5000
Step-by-step explanation:
I need help on my homework.
Answers
Answer:
[tex] \frac{3}{4} > \frac{ - 2 + 2x}{4} \\ \\ (4 \times) \frac{3}{4} > \frac{ - 2 + 2x}{4} ( \times 4) \\ \\ 3 > - 2 + 2x \\ \\ 3 + 2 > - 2 + 2 + 2x \\ \\ 5 > 2x \\ \\ 5 \div 2 > 2x \div 2 \\ \\ \frac{5}{2} > x \\ \\ x < \frac{5}{2} [/tex]
I hope I helped you^_^
The two triangles are similar. Find the values of the unknown variables
Answers
Answer:
x = 84 y = 59°
Step-by-step explanation:
x = (40/30)×63
x = 84
∆ABC = ∆PQR
so y = 59°
Answer:
1.) 47
2.) 28
Step-by-step explanation:
you just had to use the sin equation for both
The average price of an item is $42 with a standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation!
Answers
The mean price goes between $ 41.16 and $ 42.84, so a value of $ 48 is unusually high.
Since the average price of an item is $ 42 with a standard deviation of $ 3, to find a 98% confidence interval about the mean, and determine if a value of X = 48 is unusually high or if it is normal, the following calculations should be done:
(((42 - 3) + (42 + 3)) / 2) x 0.98 = X ((39 + 45) / 2) x 0.98 = X 42 x 0.98 = X 41.16 = X
(((42 - 3) + (42 + 3)) / 2) x 1.02 = X ((39 + 45) / 2) x 1.02 = X 42 x 1.02 = X 42.84 = X
Therefore, as the mean price goes between $ 41.16 and $ 42.84, a value of $ 48 is unusually high.
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Alan has $400 in his checking account. He withdraws $50 each week. The amount remaining in his account, f(x), after x weeks is
represented by a function. What is the range of the function?
Answers
Answer:
{0, 50, 100, 150, ..., 350, 400}
Step-by-step explanation:
The range of Alan's balance will be multiples of 50 that are between (and including) 0 and 400.
{0, 50, 100, 150, ..., 350, 400}
_____
The expression for f(x) is ...
f(x) = initial balance - (rate of withdrawal) × (time period)
f(x) = 400 -50x
This is a continuous linear function defined for all x, and capable of producing f(x) values between -∞ and +∞. The range of this function is "all real numbers."
However, as applied to this problem, the domain of x is the set of integers from 0 to 8. The corresponding range is multiples of 50 from 0 to 8, that is, values 0, 50, ..., 350, 400.
0.1/0.5=X/10 what is x
Answers
0.1/0.5 is the same as 1/5
1/5 = X/10
we times both sides by 10 to get x on its own
1/5 x 10 = 10/5 = 2 ( which equals X/10 x 10)
X/10 x 10 = X
2 = X
Bidmass
Working out equations
Answers
Answer:
16
Step-by-step explanation:
5+15-8/4=
5+15-4=
16
Answer:
10/2+15-8/4= 18
Step-by-step explanation:
glad to help
3 more day till christmas
Mrs. Heath baked 56 cookies. She put an equal number of cookies into 7 bags. How many cookies did she put in each bag?
Answers
Answer:
8
Step-by-step explanation:
you have to divide 56 by 7 and you will get 8.
Answer:
8
Step-by-step explanation:
You're dividing the 56 cookies into 7 bags, so you write 56 ÷ 7 = 8
Find the 57th term of the arithmetic sequence -13,-29,-47,….
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Answer:
answer -909 photo with solution is attached
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Answers
Answer:
85 percent
Step-by-step explanation:
Solve x2+6x+7=0
A.x=-1 and x=-5.
B. 3+ √2
C.-3+ √2
D. -3+ √2
———-
2
Answers
Answer:
-3+ √3 or -3- √3
Step-by-step explanation:
A bakery asks 75 customers to vote for a new bagel flavor. Onion flavor receives 33 votes. Cheddar flavor receives 42 votes. Use this information to answer the questions below. What fraction shows the proportion of customers who voted for cheddar flavor? What percent of customers voted for cheddar flavor?
Answers
Using proportions, it is found that:
The fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]56% of customers voted for cheddar flavor.A proportion is the number of desired outcomes divided by the number of total outcomes.A percentage is the proportion multiplied by 100%.In this question, 42 out of 75 customers voted for the cheddar flavor, hence:
[tex]p = \frac{42}{75}[/tex]
That is, the fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]
The percentage is:
[tex]\frac{42}{75} \times 100\% = 56\%[/tex]
56% of customers voted for cheddar flavor.
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2. Mark works as a consultant for a computer firm. His weekly income is $425. His
monthly expenses are $1,266. How much does he have left for variable expenses?
(Hint: There are four pay periods in one month.)
Answers
Hi there, I hope you understand my answer and that it is correct :)
So, First we multiply $425 by 4 because there are approximately 4 weeks in every month, so as shown [tex]425*4=1,700[/tex]
____________________________________________________________
Next We subtract the answer, which we got to be 1,700 from 1266.
[tex]1700 - 1266=434[/tex]
____________________________________________________________
Answer : $434 left to spend :)
How much water do you need to add to make each concentration?
1% sugar syrup using 12 g sugar
Answers
Answer:
1188 grams of water
Step-by-step explanation:
x is the grams of water
so total is 12+x grams
sugar/total is 12/12+x
and 1% ratio is 12/12+x=1/100
so x would be 1188 grams of water.
Answer:
1188
Step-by-step explanation:
Start with the part and whole proportion
[tex]\frac{12}{?} =\frac{1}{100}[/tex]
multiply the one by 12 and 100 by 12
[tex]\frac{12}{1200} =\frac{1}{100}[/tex]
now subtract 12 from 1200
then you get 1188.
I hope this helps :))
Nineteen less than twice a number is greater than the number added by four
Answers
Answer:
2x - 19 + x + 4
Step-by-step explanation:
2x - 19 + x + 4
Write as the opposite of a square root. -3√5
Answers
Answer:
3x5² is the opposite of ur uestion
The value of -3√5 as the opposite of the square root is -75.
What is square root?The factor of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9.
Given:
-3√5
The opposite of the square root is the square, so,
-3√5 = -3 × 5²
-3√5 = - 3 × 25
-3√5 = - 75
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let f(x)=3x-2, g(x)=5x+1
fogof(2)
Answers
Answer:
f(g(2)) = 29
Step-by-step explanation:
First of all we write the new function defined as the composite function of f and g: f(g(x)) = 3(5x+1) - 2 = 15x + 3 - 2 = 15x -1
Now we can simply "plug in" 2 instead of the x in the function we just obtained: f(g(2)) = 15*2 - 1 = 29
Mrs. Montgomery earns a 6.5% commission on her total sales. Last month, she had sales of $55,780. How much commission did Mrs. Montgomery earn last month?
Answers
Answer:
3625.7
Step-by-step explanation:
hope that will help goodbye
will give brainliest due in 20 min
Answers
Answer:
25 is the area of ABCD
Step-by-step explanation:
5×5 = 25
Show that the equation y + 8 = 2(4x + 4) is linear and that it represents a proportional relationship between x and y.
Answers
Answer:
Step-by-step explanation:
y + 8 = 8x + 8
Subtract:
(3x^3– 10x^2+ 13x) – (5x^3+ 4x² – 9x)
A. 8x^3 + 14x^2 - 22x
B. 8x^3 - 6x^2 + 4x
C. 2x^3 - 6x^2 - 4x
D. -2x^3 - 14x^2 + 22x
Answers
Answer:
D
Step-by-step explanation:
(3x³ - 10x² + 13x) - (5x³ + 4x² - 9x)
3x³ - 10x² + 13x - 5x³ - 4x² + 9x Change all terms after the subtraction sign to
the opposite sign (definition of Subtraction)
(3x³ - 5x³) + (-10x² - 4x²) + (13x + 9x) Group like terms together
-2x³ - 14x² + 22x
Pls HELPPPPPP!! the answer
Answers
( -2,1 )
Hope it helps
Have a good day!!
:))))))
The length of a rectangular garden is 3 feet more than 2 times the width. The perimeter of the garden is 48 feet. Find the length and width of the garden .
Answers
Answer:
length 17 feet
width 7 feet
Step-by-step explanation:
Let w represent the width. Then the length is 2w+3, and the perimeter is ...
P = 2(L +W)
48 = 2((2w+3) +w) = 6w +6
42 = 6w
7 = w . . . . . . . . width
(2w+3) = 17 . . . length
The length of the garden is 17 feet; its width is 7 feet.
Someone help please
Answers
It is 4pi/7, or b. Just want to help ;)