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

From 24 grams to 96 grams ( percent change )

Answers

Answer:

i think it is 300%

Step-by-step explanation:

(URGENT!! PLS HELP) The color of paint used to paint a race car includes a mixture of yellow and green paint. Scotty wants to lighten the color by increasing the amount of yellow paint 30%. If a new mixture contains 3.9 liters of yellow paint, how many liters of yellow paint did he use in the previous mixture?

Answers

Answer:

3 liters

Step-by-step explanation:

Let the initial amount of yellow paint be x

Then we have x increased by 30% equals 3.9 liters:

x + 0.3x = 3.91.3x  = 3.9x = 3.9/1.3x = 3 liters

Find the value of x so that line m is parallel to line l.

Answers

Answer:

-17

Step-by-step explanation:

The angles are corresponding angles so when the lines are parallel, the lines are equal

3x-12 = 4x+5

Subtract 3x from each side

3x-12 -3x = 4x+5-3x

-12 = x+5

Subtract 5 from each side

-12 -5 = x+5-5

-17 = x

Answer:

-17

Step-by-step explanation:

The two angles that are shown are *corresponding angles* which means they lie in the same spot, just on two different parallel lines. They are congruent angles. Therefore, you should set up an equation to solve for x. Since the two angles are congruent, you should set the expressions equal to each other. 3x-12=4x+5.

Th e NCAA recommends that a competition diving pool intended for use with two 1-m springboards and two 3-m springboards, in addition to diving platforms set at 5 m, 7.5 m, and 10 m above the water, have a width of 75 ft 1 in., a length of 60 ft, and a minimum water depth of 14 ft 10 in. What is the minimum volume of water such a pool would hold in cubic yards, to the nearest whole number?

Answers

Answer:

The volume of the swimming pool is approximately 2475 yd³ to the nearest whole number

Step-by-step explanation:

The given information are;

The width of the swimming pool = 75 ft. 1 in.

The length of swimming pool = 60 ft.

The depth of the swimming pool = 14 ft. 10 in.

Therefore;

The volume of the swimming pool = Width × Length × Depth

The volume of the swimming pool = 75 ft. 1 in. × 60 ft. × 14 ft. 10 in.

The volume of the swimming pool = 901 in. × 720 in. × 178 in. = 115472160 in.³

1 in.³ = 2.14335 × 10⁻⁵ yd³

∴ 115472160 in.³ = 115472160 in.³  × 2.14335 × 10⁻⁵ yd³/in³ ≈ 2474.969 yd³

Which gives;

The volume of the swimming pool ≈ 2475 yd³ to the nearest whole number.

A circuit board manufacturer rejects a 100-ohm resistor if its measured resistance is 0.15 ohm or more away from 100 ohms. Resistors A and B are rejected. Resistor A's resistance differs from 100 ohms by +0.15 ohm. Resistor B's resistance differs from 100 ohms by -0.78 ohm. Which resistor has a resistance closer to 100 ohms?

Answers

Answer:

Resistor A has a resistance closer to 100

Step-by-step explanation:

Here, we want to know which of the two resistors have a resistance closer to 100 ohms

To know the resistance closer to 100, we need to know the absolute value of the resistances

-0.78 has a resistance of 100 - 0.78 = 99.22

The 15 ohms resistor has resistance of 100 + 0.15 = 100.15

Since 100.15 is closer to 100 than 99.22, due to the absolute value of both, then the +0.15 ohm resistor is closer to 100

How do I factor
x ^5−x^ 4+3x−3

Answers

Answer: look at picture

Find the average rate of change of g(x)=3x^2 ver the interval [-5, -3].

Answers

Answer:

ill help

Step-by-step explanation:

Help? Find angle psw

Answers

The angle is about 80°

What is the equation of this line?
A. y=43x−4

B. y=34x−4

C. y=−4x+34

D. y=−4x+43

Answers

Answer:

Y=4/3x - 4

Step-by-step explanation:

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the given line is y=(4/3)x-4.

What is the equation of a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The slope of the line can be calculated with the two points that are present on the line, in this case, these points are (3,0) and (0, -4). Therefore, the slope is,

Slope, m = (-4 - 0)/(0 - 3) = -4/-3 = 4/3

The y-intercept of the line is -4, therefore, the equation of the line can be written as,

y = mx + c

y = (4/3)x - 4

Hence, the equation of the given line is y=(4/3)x-4.

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find the area of the equilateral triangle.if its perimeter is 24cm​

Answers

Answer:

16√3 cm²

Step-by-step explanation:

The perimeter of a triangle is the sum of its all three sides. Since this is an equilateral triangle, all sides are equal.

Let's consider one side of the triangle to be 'x'

Givent that, the perimeter is 24cm,

The equation should be x + x + x = 24

⇒3x = 24

∴ x = 8 cm

To find the area of the triangle, we need to find the height, and for that, we can use trigonometry.

Since it is an equilateral triangle, all angles are exact 60°.

let's draw a line and mark it as 'h'.

we can use sine formula to find out the opposite i.e. h

sin∅ = opposite ÷ hypotaneous

sin 60° = h ÷ 8

h = 8 sin 60°

h= 4√3

Now, let's find the area

Area = 1/2 × base × height

Area = 1/2 × 8 × 4√3

area= 16√3 cm²

What is the name of the lake located at letter B on the map above? Answer is C :)

Answers

Answer:

the answer is C. lake Texoma

hope this helps

Two-Step Equations 2/5x−3=−17

Answers

Answer:

x =-35

Step-by-step explanation:

2/5x−3=−17

Add 3 to each side

2/5x−3+3=−17+3

2/5x = -14

Multiply each side by 5/2

5/2 * 2/5x = -14 * 5/2

x = -35

Answer:

x = -35

Step-by-step explanation:

Add 3 to each side, so it now looks like this: 2/5x = -14Divide each side by 2/5 to cancel out the 2/5 next to x. It should now look like this: x = -35

I hope this helps!

x - 13 = 22 linear equations

Answers

Answer:

x = 35

Step-by-step explanation:

x - 13 = 22

Add 13 to each side

x - 13+13 = 22+13

x = 35

See attachment for math work and answer.

A rectangular tank has a length of 12 feet, width of 8 feet, and height of 5 feet. Frankie filled the tank with water at a rate of 4 cubic feet per minute. At this rate, how long will it take Frankie to completely fill the tank without overflowing it?

Answers

Answer:

Step-by-step explanation:

12 x 8 x 5 = 480/4= 120 minutes or 2 hours  

Carson was shopping online for bow ties to wear with his school uniform he bought a certain number of ties that each cost $12.50 and paid a flat rate of 19 for shipping and handling he has 220 in his bank account before buying the tie write the expression to represent how much money Carson spell on low tide be sure to Define your variable

Answers

Given :

Carson was shopping online for bow ties to wear with his school uniform he bought a certain number of ties that each cost $12.50 and paid a flat rate of 19 for shipping and handling.

He has $220 in his bank account before buying the tie.

To Find :

Maximum number of ties he can buy.

Solution :

Let, price of buying x ties is y.

y = 19 + (12.50)x

It is given that he has $200 in his bank account.

So, price of buying tie ≤ $200

y ≤ 200

19 + (12.50)x ≤ 200

(12.50)x ≤ 200 - 19

x ≤ 14.48

Since, number of tie cannot be in decimal.

x ≤ 14

Therefore, maximum tie he can buy is 14.

Hence, this is the required solution.

I went to the grocery store to buy avocados. They were $3 for 4. How much will it cost me for 10?

Answers

Answer:

7.50$

Step-by-step explanation:

3+3+1.5=7.50$.

PLEASE HELP!! MATH FINAL + NO EXPLANATION NEEDED :))

Answers

F(x+6) +2 up and right in a graph is positive

Answer:

C.

Step-by-step explanation:

55 > 5x + 5 > -25
pls help

Answers

hejdjdjkdjdidjfjjfjejdjdhdijdjdhdhdidhdidjdidhudieiruridiehidhjbfjrjjd

please please please i need help !!!

Answers

Answer: Choice B

h(c) = 1 for at least one c between -3 and 4

====================================================

Explanation:

Draw an xy axis system. Plot the points (-3,-1) and (4,2) on this grid. These points come from the fact that h(-3) = -1 and h(4) = 2. These are the endpoints of the h(x) function.

Next, draw horizontal lines through both points. Also, draw vertical lines through the two points as well. A rectangle will form.

The region inside this rectangle is all we care about.

We're told that h(x) has endpoints mentioned earlier, and h(x) is continuous, so that means we have some curve or line through the two points. One such example is shown below. There are infinitely many possible curves to draw out as long as they stay in the rectangle.

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

After you have your h(x) function curve drawn, draw a horizontal line through y = 1 on the y axis. This is the dashed line in the diagram below.

This horizontal line crosses the green h(x) curve at one point or more. In my example, it does so at one point only. However, you could easily draw h(x) so that it crosses y = 1 as many times as you want (just have it squiggle up and down multiple times).

This shows that h(c) = 1 is possible when [tex]-3 \le c \le 4[/tex]. Here c is playing the role of x since it is the input of a function. The h(c) is the output, so that's the y value.

This says that for some input between -3 and 4, it's possible to get an output of 1.

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

Here's a real world example of the intermediate value theorem.

Let's say the endpoints are A and B, and they are two towns.

The h(x) curve is a road connecting the towns.

To go from A to B, or vice versa, we need to cross over some border that is between the towns. The border in this case is the dashed horizontal line in the diagram.

side note: A special use of the intermediate value theorem is to show that a root exists on some interval (if you know the function changes between positive to negative, or vice versa).

If you are given the graph of a line and are asked to write the equation of a
perpendicular line, does it matter what the y-intercept will be for the equation
you write? Explain why or why not.

Answers

Answer:

Yes

Step-by-step explanation:

It does matter because when it comes to perpendicular lines the equations for the lines with have opposite y-intercepts. So if you had y=2x +3 the perpendicular line would be y=-1/2x +3.

Yes, the y-intercept of the equation written does matter and can be determined if a point on the line is given.

According to the question;

We are required to determine; does it matter what the y-intercept will be for the equation you write when given the graph of a line and are asked to write the equation of a perpendicular line.

Although, according to line geometry;

The slope of two perpendicular lines are related as follows;

m1 m2 = -1

The y-intercept of the perpendicular line does matter when writing the equation of the line and can be determined if a point on the perpendicular line is given.

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Choose the equation below that represents the line passing through the point (−2, −3) with a slope of −6​

Answers

Answer:

a

Step-by-step explanation:

:)

A.

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

Hanna will spend $150 on music festival tickets. Reserved seat tickets cost $25 and general admission tickets cost $10. She wrote the following to represent the situation with a linear equation. What kind of equation did she use?

Answers

Answer: Standard Form

Step-by-step explanation:

In the slope intercept form, you can only solve for one equation at a time.

Ex: y = -2.5x + 15

but when using standard you can easly get the answer for both ticket prices

Ex: 25x + 10y = 150

5r + 2g = 30 is the linear equation that best describes the scenario.

What is a Linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given this, Hanna will spend $150 on music festival tickets. Reserved seat tickets cost $25 and general admission tickets cost $10.

Let "r" be the Number of reserved tickets she bought

and "g" be the number of  general admission tickets she bought

Money spent od reserved ticket = 25 * r

Money spent in general tickets = 10 *g

Since she totals spent 150$

Thus, the equation will be

25r + 10g = 150

Divide by 5 into both the sides

5r + 2g = 30

therefore, The linear equation that represents the given situation is 5r + 2g = 30.

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36÷2/3

pls help i no understand

Answers

It would be 54.
Easiest way to do this is to put 36 over 1. Then cross multiply and get 3(36)/2(1) which is 108/2 and that comes out to 54.

Michael rents a car for one day. The charge is $30 plus the $0.12 per mile. He wants to spend exactly $105. How many miles can he drive?

Answers

Answer:

He can drive 625 miles

Step-by-step explanation:

Total spent: $105

$105- $30 charge = $75

$75/$0.12 per mile charge

= 625 Miles

please help me out!!!

Answers

850 because if they are 0.004 gigs and you have 3.4 you just have to divide

Can anyone please help me with this?

Answers

Slope is 4 and y intercept is -2
slope is 5/2 (rise over run) and y-intercept is -2

5. It is a method of describing a set, in words.
A. Roster Notation
C. Set Builder Notation
B. Listing Method
D. Verbal Description Method​

Answers

The correct answer choice is D. Hope this helps!!

Answer

There are two common ways of describing or specifying the members of a set: roster notation and set builder notation. These are examples of extensional and intensional definitions of sets, respectively

( need help asap for a test) Ms. Smith bought a 5 pound bag of candy for her 6th grade classroom. She gave away 2 pounds of candy to her students during the first unit of instruction and ate 6 ounces of candy during planning.

(16 ounces = 1 pound)

How many ounces of candy does Ms. Smith still have in her bag?

A.
38 ounces

B.
42 ounces

C.
48 ounces

D.
54 ounces

Answers

Answer:

c

Step-by-step explanation:

5-2=3 3•16=48 48-6=42

Q: What is the measure of <8?
A)45
B)55
C)155
D)135
Please needed help asap!

Answers

Answer:

your answer should be, D.135

i hope this helps!

Answer:

D) 135

Step-by-step explanation:

--------------- = 180 degrees

It's split and the other half is 45 degrees.

All you have to do is subtract.

180-45=135

<8 = D) 135

a) What is y=mx+b?
b) What does the m stand for?
c) What does the b stand for?
d) Where do I find the x & y?
e) If I get two coordinate points how do I find the slope? What is the formula?
f) If I get a graph, how do I find the slope?

Answers

a) y=mx+b is slope intercept form.

b) the m is the slope of the line.

c) the b is the y-intercept

d) the x-axis is horizontal, the y-axis is vertical.

e) m = rise/run = y2-y1/x2-x1

f) pick 2 points on the graph & determine their coordinates. find the difference in the y-coordinates (the rise) & the difference in the x-coordinates (the run) & divide them.
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