If the pth term of an A.P. is q and the qth term is p. Prove that its nth term is (p+q-n). ​

Answers

Answer 1
Given:

pth term of an AP = q

qth term = p

Prove:

nth term of A.P. is (p+q-n). ​

Proof:

We know that,

nth term of an AP (an) = a + (n - 1)d

Hence,

⟹ a + (p - 1)d = q

⟹ a + pd - d = q

⟹ a = q - pd + d -- equation (1)

Similarly,

⟹ a + (q - 1)d = p

Substitute the value of a from equation (1).

⟹ q - pd + d + qd - d = p

⟹ qd - pd = p - q

⟹ - d(p - q) = p - q

⟹ - d = 1

⟹ d = - 1

Substitute the value of d in equation (1).

⟹ a = q - p( - 1) + ( - 1)

⟹ a = q + p - 1

Now,

an = q + p - 1 + (n - 1)( - 1)

⟹ an = q + p - 1 - n + 1

⟹ an = p + q - n

Hence, Proved.

I hope it will help you.

Regards.

Answer 2

Step-by-step explanation:

ANSWER

pth term = q

a+(p−1)d=q

qth term = p

a+(q−1)d=p

Solving these equations, we get,

d=−1

a=(p+q−1)

Thus,

nth term = a+(n−1)d=(p+q−1)+(n−1)×(−1)=(p+q−n)


Related Questions

what is the value of r in the equation r+6=14?

Answers

Answer:

r = 8

Step-by-step explanation:

Given

r + 6 = 14 ( subtract 6 from both sides )

r = 8

You subtract 6 from 14 and you’ll get 8 so r=8

The formula for the perimeter of a rectangle is P=2(l+w). Solve for l.

Answers

Answer:

l = [tex]\frac{P-2w}{2}[/tex]

Step-by-step explanation:

Given

P = 2(l + w) ← distribute right side

P = 2l + 2w ( subtract 2w from both sides )

P - 2w = 2l ( isolate l by dividing both sides by 2 )

[tex]\frac{P-2w}{2}[/tex] = l

Answer:

l=‒2w+p/2

Step-by-step explanation:

p=2(L+w)

p=2L+2w(add ‒2w on both sides)

‒2w+p=2L+2w-2w

‒2w+p=2L

‒2w+p/2=2L/2

L=‒2w+p/2

i hope it helps you.

Luke can purchase a 10-pound item from several different stores. Which of the following is the best buy?

Answers

What are the options

Answer:

What are the stores & the data?

Two friends operate a trucking company that delivers Goods across three states they lose $24.50 each time a customer chooses to make a delivery with a competitor? Which expression shows the amount that the trucking company makes if P people use a competitor for delivery and the company makes $3,125 before the competition is considered

Answers

Answer:

3,125; 24.5p

Step-by-step explanation:

Answer:

3125-24.5p       and 2,978

Step-by-step explanation:

Given m 1= 65, find the measure of each missing angle.Givd your reasoning

Answers

Answer:

Step-by-step explanation:

Given:

m∠1 = 65°

Since. ∠1 and ∠2 are the angles of linear pair,

m∠1 + m∠2 = 180°

65° + m∠2 = 180°

m∠2 = 115°

m∠1 = m∠3 [Vertical angles]

m∠3 = 115°

Since, ∠1 and ∠4 is the linear pair of angles,

m∠1 + m∠4 = 180°

65° + m∠4 = 180°

m∠4 = 180 - 65 = 115°

m∠4 + m∠5 = 180° [Consecutive interior angles between the parallel lines]

115° + m∠5 = 180°

m∠5 = 180° - 115° = 65°

m∠5 + m∠6 = 180° [Linear pair of angles]

65° + m∠6 = 180°

m∠6 = 115°

m∠5 = m∠7 [Vertical angles]

m∠5 = m∠7 = 65°

m∠6 = m∠8 [Vertical angles]

m∠6 = m∠8 = 115°

w is no more than -7

Answers

Answer:

w≤-7

Step-by-step explanation:

No more than means it has to be -7 or less so w is no more than -7 is w≤-7

Hope this helps!

Answer:

I agree if that's what you say it mean

can someone help me with this

Answers

A ) 40

2^2=4
6^2=36
4+36=40

If Kynlee can walk 3/5 mile in 1/3 of a day, how far can she walk in 1 day.

Answers

Answer:

1 and 4/5 mile or 1.8 miles

Step-by-step explanation:

You would multiply 3/5 by 3 because in 1/3 day she can walk 3/5 miles, you want to find out how much she can walk in a day! Hope this helps! If you liked this answer, a brainliest would much be appreciated!

Answer:

9/5 i believe ( or 1 4/5 )

Step-by-step explanation:

multiply 3/5 by 3, since 1/3 is only a part of the day

( im sorry if this is wrong :( )

Guys Please HELP ME
If you give me answer quickly, I'll give you brainliest. Please help me (20 points)

Questions
1. Find the density of a cylinder with a height of 4mm, a radius of 4mm, and a mass of 250g

2. Find the density of a sphere with radius of 2m and a mass of 2kg

Answers

Answer:

Step-by-step explanation:

1st one is 62.5 kilogramic meter

2nd one is 1 kilo kilogram/cubic meter

Step-by-step explanation:

1)First calculate the volume

v=Pir²h

v=3.15×4²×4

v=201mm³

p=m/v

p=0.250/0.201

p=1.24Kg/m³

2)v=3/4pi r³

v=3/4×3.14×2³

v=33.5m³

p=m/v

p=2/33.5

p=0.0597kg/m³

I need help asap for these answers

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Go to Desmos calculator

I need help this is my last page

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Answer:

The number: 85     factors: 17, 1

Step-by-step explanation:

136-51=85

85 and 51

Common factors of 85 and 51

17,1

What is the solution to 4 x + 6 less-than-or-equal-to 18?

help
<3

Answers

Answer:

x is less-than-or-equal to 3

Step-by-step explanation:

4(3)+6 =18

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Answers

y^3/4x

Step-by-step explanation:

here,

6x^2/5y *(y^3/4x)

3xy^2/10

The length of the rectangle is four times it’s width. The rectangle has an area of 1024cm2. What is the width of the rectangle

Answers

Answer:

Length = 4 times width

Area = length * width

=(4w)w

=4w²

So 4w²=1024 cm² (given)

w²=1024/4=256

w=√(256 cm²)

=16 cm (reject negative value of square-root)

Step-by-step explanation:

Hope this helps you

Crown me as brainliest:)

Which could be the first step of an indirect proof of the conditional below?
If x2 = 25, then 5’2= 25 and x = 5,
A. Assume x=5 is true.
B. Assume 52 = 25 is true,
C. Assume x2 + 25 is true.
D. Assume 52.25 and x + 5 are true,

Answers

Answer

Option D

Step-by-step explanation

For further help (727) 335-8234

The first step of indirect proof of the conditional below

If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.

Option B is the correct answer.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Conditions:

x² = 25 then 5² = 25 and x = 5

If we have to prove the above conditions indirectly, we have to prove that x² = 25 using the conditions 5² = 25 and x = 5.

So,

We have to assume,

Step 1:

5² = 25

Step 2:

x = 5

Step 3:

x² = 25

Thus,

The first step of indirect proof of the conditional below

If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.

Option B is the correct answer.

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g(-3)=

Answers

Answer:

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Answer:

Step-by-step explanation:

What are the slope and the y-intercept of the linear function that is represented by the table?
Х
3
4
y
1
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2
1
2
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NICO
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1/4

Step-by-step explanation:

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Determine if the following is a PROPORTIONAL
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Step-by-step explanation:

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Answers

Answer:

Option 2

Step-by-step explanation:

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Answer:

you did not out the full equation so I am not able to solve your problem.

If you put the full problem I will try to solve and walk you through it.

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Step-by-step explanation:

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Step-by-step explanation:

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A hot air balloon ascended at the rate of
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Answers

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Step-by-step explanation:

7. When rice is prepared, the amount of rice varies directly as the amount of water
required. If 2 cups of rice requires 4.5 cups of water, what is the total number of cups
of water needed to prepare 5 cups of rice?

Answers

Answer:

11.25

Step-by-step explanation:

Multiply 4.5 by the reciprocal of 2/5, which is 5/2. You will then get 11.25. Hope this helped :)

Total number of cups of water needed to prepare 5 cups of rice are 11.25.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

When rice is prepared, the amount of rice varies directly as the amount of water required.

And, 2 cups of rice requires 4.5 cups of water.

Now,

Since, 2 cups of rice requires 4.5 cups of water.

Hence, For 1 cup of rice, number of cups of water = 4.5 / 2

                                                                             = 2.25

So, For 5 cups of rice, number of cups of water = 5 x 2.25

                                                                          = 11.25

Thus, Total number of cups of water needed to prepare 5 cups of rice are 11.25.

Learn more about the ratio visit:

https://brainly.com/question/25927869

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What quadrant is point A located in?
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Answers

D, Quadrant II, hope this helps :)

Describe how to find the measure of the exterior angle.

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Add sums of measures of 2 remote interior angles.

what are all the factors of 21?

Answers

Answer:

1, 3, 7, 21

p-by-step explanation:

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