The first and last terms of an AP are 7 and 49 respectively. If sum of all terms is 420, find its common difference.​

Answers

Answer 1

 Common Difference = 3 

Step-by-step explanation:

Given:

First term of AP is 7.

Last term of AP is 49.

Sum of all terms of AP is 420.

To Find:

What is the common difference of the AP ?

Solution: Let the common difference and number of terms of AP be d and n respectively.

a = first term = 7

d = common difference

l = last term = 49

Sⁿ = sum of all terms = 420

As we know that , Sum of n term of an AP is

★Sⁿ = n/2 × ( a + l ) 

⟹ 420 = n/2 ( 7 + 49 )

⟹ 420 × 2 = 56n

⟹ 840/56 = n

⟹ 15 = n

So the given AP series contains 15 terms and last term of AP will be given by -

➙ a + (n – 1)d = 49

➙ 7 + (15 – 1)d = 49

➙ 14d = 49 – 7

➙ d = 42/14

➙ d = 3

Hence, the common difference of AP series is 3.


Related Questions

According to the chart above, which of the following events occurred in Los Angeles between 1970 and 2000?
I. The white population increased.
II. The Hispanic and black populations increased.
III. The total population increased.
IV. Non-whites became a majority in the city.
A.
III. and IV. only
B.
I., II., and III. only
C.
II., III., and IV. only
D.
I., II., III., and IV.

Please select the best answer from the choices provided.

A
B
C
D

Answers

Answer:

A

Explanation:

took the test

Answer:

A) III. and IV. only

Explanation:

III. The total population increased.

IV. Non-whites became a majority in the city.

Solve the linear equation x + 3 + x - 8 + x = 55. State the property that justifies your first step and why you chose it

Answers

The equation can be solved by combining like terms. This is an example of the Associative Property because it states that the order of operations does not matter when grouping terms together. In this case, it allows us to add all of the x terms together and all of the constants together.

Therefore, the solution is x = 40.

The silicate mineral that is found in the greatest variety of igneous rocks of various compositions is ________.

Answers

The silicate mineral that is found in the greatest variety of igneous rocks of various compositions is Plagioclase.

ABOUT PLAGIOCLASE

Plagioclase is a mineral that belongs to the feldspar group. In Bowen's reaction, plagioclase is in a continuous series. From Bowen's reaction we can also know the process of crystal formation from plagioclase. The plagioclase crystallization process begins with plagioclase-Ca which gradually reacts with the remaining solution until it changes its composition towards plagioclase-Na. This change reaction is called the solid solution series, which means that the crystallization of plagioclase-Ca-plagioclase-Na will continue if it is in an equilibrium state. The chemical formula of plagioclase mineral is NaAlSi3O8-CaAl2Si2O8.

From the Bowens reaction, we can know the process of crystal formation from this plagioclase itself, in which the sequence of crystallization of plagioclase minerals is in a continuous series. The crystallization of plagioclase-Ca in the initial phase was gradual by reacting with the remaining solution, changing its composition from plagioclase-Na. The reaction of this change, plagioclase change is a solit-solution series which is a continuous reaction, meaning that the crystallization of plagioclase-Ca ---- plagioclase-Na (Anorthit ---- Albit ) if in equilibrium will continue continuously.

Learn more about Plagioclase at https://brainly.com/question/29981351.

#SPJ4

Impact of humanitarian aid on Yemen
At least one paragraph

Answers

Explanation:

222²behind h ejjejwjwjjwkwke8hf

Answer:

Yemen is the largest humanitarian crisis in the world, with more than 24 million people – some 80 per cent of the population – in need of humanitarian assistance, including more than 12 million children.

Que e Qué es un bioma regiones que comparten idénticas características del oscilación térmica conjunto de formas que moldean la corteza del nombre de que reciben los movimientos de la Tierra

Answers

Answer:

Comunidad de flora y fauna que ocupa un hábitat importante.

Explicación:

El bioma se define como una gran comunidad natural de flora y fauna que ocupa un hábitat importante como el bosque o la tundra, etc. Las plantas y los animales que viven en un bioma tienen características y adaptaciones comunes para el medio ambiente. Hay siete biomas presentes en la tierra, es decir, tundra, matorrales, bosques lluviosos, pastizales, desiertos, bosques caducifolios templados y bosques de coníferas. Hay cinco tipos principales de biomas: acuático, pastizal, bosque, desierto y tundra. Las plantas y los animales presentes en cada bioma se adaptan a ese bioma.

A ________ is an erosional feature specifically produced by alpine glaciation.
Lateral moraine
Drumlin
Crevasse spur
U-shaped valley

Answers

A U-shaped valley is an erosional feature specifically produced by alpine glaciation. Hence, the correct option is (D).

What Is An U-Shaped Valley?

A U-shaped valley is a form of natural appearance that is usually called glacial troughs. This U-shaped valley can be formed from the process of alpine glaciation. Alpine glaciation itself is basically the process of moving ice on the earth's surface due to the force of gravity. This U-shaped valley is usually found in mountains and one of the U-shaped valleys that many people know is Nant Ffrancon in Wales. This U-shaped valley also often extends to meet salt water and this valley can become an inlet of the sea.

The question is incomplete, but most probably your question was:

A ________ is an erosional feature specifically produced by alpine glaciation.

A. Lateral moraine

B. Drumlin

C. Crevasse spur

D. U-shaped valley

Learn more about U-shaped valley at https://brainly.com/question/2112700

#SPJ4

It rain maximum in pokhara valley?why give reason​

Answers

Answers: South-East part of Pokhara is opened and it has git the mountain in the southern part. That is why Pokhara receives the highest amount of rainfall in Nepal.

molten rock above ground is called (4 points) group of answer choices magma metamorphic sedimentary lava

Answers

Molten rock above ground is defined as lava, magma, or molten rock that is exposed on the earth’s surface. The molten rock above ground can be found in volcanoes, fissures, or other openings in the earth’s surface.

Lava is molten rock that has been ejected from a volcano and has cooled and hardened on the surface. Lava is usually composed of basalt, andesite, or rhyolite. It can be found in various forms, such as pahoehoe and aa. Lava is the most common form of molten rock found above ground.

Magma is molten rock that is still beneath the surface of the earth. It is composed of molten rocks, minerals, and gases that are found within the earth’s mantle and crust. Magma is the source of most volcanic eruptions and is formed when hot rocks deep within the earth melt.

Metamorphic rocks are formed when magma and other rocks are subjected to heat and pressure, which causes them to change in form. Metamorphic rocks are usually found near volcanoes and can be a combination of igneous, sedimentary, and metamorphic rocks.

Sedimentary rocks are formed when pieces of rock are broken down by water and wind and then compacted and cemented together. Sedimentary rocks are usually composed of sand, gravel, or mud and can be found near the earth’s surface.

Learn more about Lava at :https://brainly.com/question/15393639

#SPJ4

1. Con sus palabras diga las diferencias entre ecosistemas, población y
comunidad y de ejemplos de cada uno.
2. Cuál es la diferencia entre un ecólogo y un ecologista.
3. Nombre los factores bióticos y los factores abióticos.
4. Que relaciones existen entre los miembros de un ecosistema (competencias y
cooperación), de cada uno explicar y dar un ejemplo. (nombra mas tipos de
relaciones fuera de las que están en la presentación de p.p.)

Answers

Answer:

100 POINTS!!! PLEASE SHOW YOUR WORK. I WANT TO UNDERSTAND IT

5 QUESTIONS

1) Pedro wants to make a 35% sugar solution. He has 3 ounces of a 56% sugar. How many ounces of a 14% sugar solution must he add to this to create the desired mixture?

2) Xavier wants to make 10 gallons of a 42% saline solution by mixing together a 50% saline solution and a 10% saline solution. How much of each solution must he use?

3) A passenger on a plane made a trip to Portland and back/ The plane took the same route coming back. On the trip there it flew 210 kilometers per hour and on the return trip it went 280 kilometers per hour. If the total trip took 5 hours, how long did the trip take coming back?

4) Amanda and Alexis live 4 miles apart. They decide to start walking toward each other's houses at the same time. Amanda walks at a rate of 3.5 miles per hour and Alexis walks at a rate of 4 miles per hour. How long will it take for them to meet?

5) Working alone, Juan can harvest a field in 13 hours. Shayna can harvest the same field in 14 hours. Find how long it would take them if they worked together.

I need help solving this question

Answers

Index fossils are fossils used to define and identify geologic periods. Scientists can estimate the ages of rock if they contain certain index fossils. Option D

What are index fossils.?

Generally, Index fossils are the remains of creatures that existed during a certain time period and were found in a variety of locations around the globe.

They may be used as a tool to assist in establishing the age of the rock strata in which they are discovered. Index fossils may be used to link rock layers from various regions and to estimate the relative age of rocks.

This is made possible by the fact that index fossils can be discovered in many different locales. They are often used in the field of biostratigraphy, which refers to the study of the temporal succession of fossils found in alternating strata of rock.

Read more about index fossils.

https://brainly.com/question/14988327

#SPJ1

3. The countries shaded in the map below represent.
15 points
Use the map below and your knowledge of social studies to answer the
following question.
A. USMCA (United States Mexico Canada Agreement)
B. EU (European Union)
C. ASEAN (Association of Southeast Asian Nations)
D.OPEC (Organization of Petroleum Exporting Countries)

Answers

B. EU (European Union)

How did the ENIAC change computing?

Answers

The ENIAC change computing used thousands of tubes to complete tasks in the right order.

One of the earliest computers ever built was the ENIAC. The Ballistic Research Laboratory of the US Army primarily used ENIAC to create artillery firing tables. The computer commenced functioning on December 10, 1945. ENIAC could compute a trajectory in 30 seconds as opposed to a person needing 20 hours to do it.

Despite this, ENIAC became the most capable calculator ever created. It was the first electrical digital computer that could be programmed for ordinary use. The British Second World War computer Colossus and Charles Babbage's Analytical Engine both contained conditional branching, which allowed them to execute various instructions or change the sequence in which they were executed depending on the value of certain data.

The complete question is, "How did the ENIAC change computing?

A. It used on and off signals to give computers instructions.

B. It used thousands of tubes to complete tasks in the right order.

C. It could perform a single task perfectly

D. It could be reprogrammed to complete new tasks."

Learn more about ENIAC here:

https://brainly.com/question/28565456

#SPJ4

How did Mapp v. Ohio set a legal precedent?
1. The Supreme Court’s ruling extended the exclusionary rule to state courts.
2. The Supreme Court’s ruling made it legal to own por..graphy.
3. The Supreme Court’s ruling allowed officers to enter homes within reason.
4. The Supreme Court’s ruling required that state courts uphold anti-gambling laws.

Answers

The case of "Mapp v. Ohio" set a legal precedent because the Supreme Court’s ruling extended the exclusionary rule to state courts. The Option 1 is correct.

Why is case of Mapp v. Ohio significant?

In Mapp v. Ohio, the United States Supreme Court ruled (6-3) on June 19, 1961, that evidence obtained in violation of the Fourth Amendment to the United States Constitution, which prohibits "unreasonable searches and seizures," is inadmissible in state courts.

In doing so, it held that the federal exclusionary rule, which prohibited the use of unconstitutionally obtained evidence in federal courts, was also applicable to states under the incorporation doctrine, the theory that most protections of the federal Bill of Rights are guaranteed against the states under the Fourteenth Amendment's due process clause, which prohibits states from denying life, liberty, or property without due process of law.

Read more about Mapp v. Ohio

brainly.com/question/13054438

#SPJ1

Rock layers close to earth's surface contain fossils grow what era

Answers

Answer :Cenozoic

Explanation:

Cenozoic. That is the era of the ice age, and dinosaur age

What government and economic system does Polynesia have?​

Answers

Answer:

Since 1962, when France stationed military personnel in the region, French Polynesia has changed from a subsistence agricultural economy to one in which a high proportion of the work force is either employed by the military or supports the tourist industry. Polynesia's government is a Parliamentary system.

What two things did Washington warn about in his farewell address ?

Answers

Washington cautions the public that political factions may endeavor to block the implementation of the government's legislation or to prevent the branches of government from executing their constitutionally granted functions.

In this letter to "Friends and Citizens," Washington cautioned that the forces of geographical sectionalism, political factionalism, and foreign involvement in internal matters jeopardized the republic's stability.

George Washington indicated in his Farewell Address that he would not seek a third term as President. --> Warns of the threat to national unity posed by the emergence of political parties and sectionalism.

Learn more about to Washington

https://brainly.com/question/14432921

#SPJ4

9. A paragraph, in your own words, explaining how Hess's accomplishments have benefited the world.

Answers

Answer:

God rested on the seventh day, so observant Jews do not work ... 1 In your own words explain how Moses and Pesach are connected . 2 ... Shabbat as a very holy time and a time for rest.

What does elevation indicate on a physical map? A) how deep the water is B) how high the ground is C) how much rainfall occurs D) how much snowfall occurs

Answers

Answer:

The answer is B, how high the ground is

In Nigeria, the under-five mortality rate is nearly 120 per 1,000 births. In the UK it is 4. Calculate how many times worse the under-five mortality rate is in Nigeria compared to the UK.

Answers

The neonatal mortality rate (NMR) and under-five mortality rate (U5MR) in Nigeria are both 39 and 120 per 1,000 live births, respectively. The under-five mortality rate in Nigeria is 30 times that of the UK.

Where is Nigeria?

Nigeria has a varied topography and equatorial climates with a wide range of humidity. Nigeria is most diversified in its population, nevertheless. English, Igbo, Fula, Hausa, Edo, Ibibio, Tiv, and Yoruba are just a few of the several languages used in Nigeria. The country is rich in natural resources, with significant deposits of petroleum and natural gas.

Abuja is located within the Federal Capital Territory, which was created by executive decree in 1976. Lagos, the nation's former capital, is still the leading commercial and industrial hub.

To know more about Topography, visit:

https://brainly.com/question/792235

#SPJ1

80°

14x + 2

The figure is a parallelogram.

Solve for x.

Answers

In the given parallelogram QRST, x = 7°.

In a quadrilateral, adjacent angles are the pair of angles, that come is formed by the intersection of any common line.

In the question, we are shown a parallelogram QRST and are asked to find the value of x.

We know that ∠TQR and ∠QRS are adjacent, as they include a common side, QR.

∠TQR = 80°, ∠QRS = (14x + 2)°

Now, we know that adjacent angles of a parallelogram are supplementary, that is their sum = 180°

∴ ∠TQR + ∠QRS = 180°

or, 80° + (14x + 2)° = 180°

or, 14x = 180° - 80° -2° = 98°

or, x = 98°/14 = 7°

∴ In the given parallelogram QRST, x = 7°.

Learn more about Parallelograms at

brainly.com/question/24056495

#SPJ4

Which of the following foods is likely a representative of indigenous culture?

Spaghetti in Ghana
Goat milk and yogurt in Afghanistan
Mango smoothies in the United States
Pepperoni pizza in Spain
French fries in Canada

Answers

Answer:

goat milk and yogurt in Afghanistan i think

The self-sufficiency model promotes development primarily by? increasing tariffs to improve government services. protecting domestic businesses from competition. encouraging consumption of domestic goods. limiting imports while encouraging exports. focusing on sectors that generate the most money.

Answers

Answer: b

Explanation:

It just makes sense, the model says to find a unique product that your countries has that everyone needs. So the model helps you find a product to put in the market, and to prevent less competition........

An das on periodt

sedimentary rocks are formed due to the (4 points) group of answer choices cooling of magma weathering of rocks changes in pressure changes in temperature

Answers

Sedimentary rocks are formed due to the weathering of rocks. Therefore the second option is correct.

Sedimentary rocks are typically formed on or near the Earth's surface, while metamorphic and igneous rocks are created deep within the planet.

The most important processes that led to their creation are:

Erosion (by water, wind, etc.)Weathering (from sunlight and other elements)Dissolution (of minerals by water or other substances)Precipitation (rainwater running off of surfaces)Lithification (the formation of rock from compressed sediment).

Common examples of sedimentary rocks include sandstonelimestone, and shale. These rocks often begin as sediments that are carried by rivers and deposited in lakes and oceans.

Know more about Rocks here:

https://brainly.com/question/30016535?referrer=searchResults

Karma is determined by, living within, or following

one's dharma.
the Vedas.
Brahma.
one's caste.

Answers

It would probably be a

Why are there products from so many different places? who benefits? and why don’t we simply make everything ourselves?

Answers

Answer:

There are products from so many different places because there is a global market for goods and services. Producers benefit from the increased demand and consumers benefit from the increased choice. There are also efficiency gains from international trade, as different countries specialize in the production of different goods and services.

hi guys i need your help please I'll give brainiest and 50 points please no links or I'll report​

Answers

1. Evaporation
2.Water Cycle
3.Cloud
4.Ground Water
5.Precipitation
6.Transpiration
7.Condensation
8.Surface Watee

Answer:

i answered on ur previous quastion

Plssssss help meeewee

Answers

Answer:

See explanation.

Explanation:

1. Neil Armstrong

2. A

Explain what a mini-state is? Give a specific example of one in Europe.

Answers

Answer:

Vatican City

Explanation:

European microstates - Wikipedia

The European microstates or European ministates are a set of very small sovereign states in Europe. The term is typically used to refer to the six smallest states in Europe by area: Andorra, Liechtenstein, Malta, Monaco, San Marino, and Vatican City.

wikipediq

Which of the following characteristics would be helpful to a geologist who is attempting to visually identify the rock makeup of an outcrop?
Choose one or more:A.the presence or absence of bedding or foliationB.the color of the outcrop's exposureC.the presence or absence of faults or foldsD.the amount and type of weathering of the outcrop

Answers

A) The presence or absence of bedding or foliation, D)the amount and type of weathering of the outcrop, C)the presence or absence of faults or folds are the characteristics that would be helpful to a geologist who is attempting to visually identify the rock makeup of an outcrop.

Understanding the composition of an outcrop is essential for any geologist. To gain an accurate insight into the rock makeup of an area, there are several characteristics to consider.

These include the presence or absence of bedding or foliation, the amount and type of weathering of the outcrop, and the presence or absence of faults or folds.

With a keen eye and knowledge of the local geology, a geologist can accurately identify the makeup of an outcrop.

In order to do this, they look for certain characteristics including the presence or absence of bedding or foliation, the amount and type of weathering of the outcrop, and the presence or absence of faults or folds.

To learn more about rock, click here:

https://brainly.com/question/26046551

#SPJ4

How have Spanish and native cultures left their marks on culture in Pacific South America?

Please help I’m so lost and i have school tomorrow

Answers

Answer:

Some major ways that Spanish and native cultures have affected Pacific South American culture are language, cuisine, and music. Majority of Pacific south America speaks Spanish and tacos, guacamole, and most salsa and corn based snacks come from hispanic culture and very popular/common in South America. There are also a huge amount of very famous hispanic musitions such as, Pitbull, Shakira, Mariah Carey, etc.

Other Questions
helppppppppppppppppppp Can anyone help me asap!? Can u pls help me, pls Can some one help me with this question its hard :( down below ill give brainliest What caused the metal shortage in the US during ww2? Pharoah Company had the following transactions during 2022: 1. Issued $355000 of par value common stock for cash. 2. Recorded and paid wages expense of $170400. 3. Acquired land by issuing common stock of par value $142000. 4. Declared and paid a cash dividend of $28400. 5. Sold a long-term investment (cost $8520) for cash of $8520. 6. Recorded cash sales of $1136000. 7. Bought inventory for cash of $454400. 8. Acquired an investment in Zynga stock for cash of $59640. 9. Converted bonds payable to common stock in the amount of $1420000. 10. Repaid a 6-year note payable in the amount of $624800. What is the net cash provided by financing activities? i have no idea pls help thats not evan an answer choise Television journalist barbara walters died on december 30. What was her first job in broadcasting? PLSSSSS HELP IK SPANISH PLSSS AND IF I GET A LINK I WILL REPORT U Seattle's Space Needle is a symbol of - cultural differences. O population growth. O advances in technology. the separation of powers. help pls Divide the following polynomials, then place the answer in the proper location on the grid. Use synthetic division. Write the answer in descending powers of x. (3x^2 +7x - 18)/(x - 3) Which of these is the absolute value parent function?A. f(x) = xOB. f(x) = 2OC. f(x) = xOD. f(x) = Ixl Which of the following is true of planning and buying TV and radio advertising? O Radio formats appeal to mass audiences, giving it more spillover than TV. O Radio ads are much more expensive to produce than TV ads. O A disadvantage of TV is that it is unable to build awareness quickly. O TV advertising takes up a lesser portion of the IMC budget as compared to radio. O TV is still the best medium to generate excitement around a brand. How did the US government use propaganda in World War II? What are the three factors of production explain and provide examples for each? A lacrosse league has 20 teams in it's first year. The number of teams in the league increases by 20.% in it's 2nd year. In the 3rd year the number of teams increases by 25% from the 2nd year. How many are in the league in the 3rd year? Most energy resources used by humans are nonrenewable. Which of the following is NOT a nonrenewable energy resource?AcoalBnatural gasCoilDwind Seeds are important to the reproduction of many kinds of plants. Some seeds, especially those dispersed by animals, are enclosed in a sweet, fleshy fruit. How would damage to the vascular tissue leading to a developing fruit affect the fruit?A.Water loss from the fruit would happen at an increased rate.B.The number of seeds enclosed in the fruit would decrease.C.The amount of water and sugar stored in the fruit would decrease.D.The raw materials needed for photosynthesis would not reach the fruit. Why is the Copernican Revolution significant?