Mathematics, 22.07.2019 08:30 heavenmckissack21

Which of the following is an arithmetic sequence? a. 1, 2, 4, 8, … b. 2, 4, 6, 8, … c. 1, 2, 4, 7, … d. 1, –3, 2, –6, … asap

Answers: 2

Show answers

Answers

Answer from: pronces

Thearithmetic sequence is $\boxed{{\mathbf{2,4,6,8, \ldots }}}$ and it matches with $\boxed{{\mathbf{OPTION B}}}$ .

Further explanation:

It is given that the four options are as follows:

$\begin{aligned}{\text{OPTION A}} \to 1,2,4,8,\ldots\hfill\\{\text{OPTION B}}\to 2,4,6,8, \ldots\hfill\\{\text{OPTION C}} \to 1,2,4,7,\ldots\hfill\\{\text{OPTION D}} \to 1, - 3,2, - 6, \ldots\hfill\\\end{aligned}$

Now, for OPTION A, the sequence is $1,2,4,8,\ldots$ .

Here, the first term ${a_1}$ is , the second term ${a_2}$ is and third term ${a_3}$ is .

The common difference is the difference of the successive term and its preceding term.

Now, check whether the common difference is same or not. If same, then the given sequence is AP else not.

$\begin{aligned}{a_2} - {a_1} &= {a_3} - {a_2} \hfill\\\,\,\,\,\,2 - 1\mathop & _=^? \:4 - 2 \hfill \\\,\,\,\,\,\,\,\,\,\,\,\,\,1 \ne2\hfill\\\end{aligned}$

Therefore, common difference is not same so it is not an arithmetic sequence so it does not matches with OPTION A.

Now, for OPTION B, the sequence is $2,4,6,8,\ldots$ .

Here, the first term ${a_1}$ is , the second term ${a_2}$ is and third term ${a_3}$ is .

Now, check whether the common difference is same or not. If same, then the given sequence is AP else not.

$\begin{aligned}{a_2} - {a_1} = {a_3} - {a_2}\hfill\\\,\,\,\,\,6 - 4\mathop =\limits^? 4 - 2\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,\,2=2\hfill\\\end{aligned}$

Therefore, common difference is same so it is an arithmetic sequence so it matches with OPTION B.

Now, for OPTION C, the sequence is $1,2,4,7,\ldots$ .

Here, the first term ${a_1}$ is , the second term ${a_2}$ is and third term ${a_3}$ is .

Now, check whether the common difference is same or not. If same, then the given sequence is AP else not.

$\begin{aligned}{a_2} - {a_1} = {a_3} - {a_2} \hfill\\\,\,\,\,\,4 - 2\mathop=\limits^? 2 - 1\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,\,2 \ne1\hfill\\\end{aligned}$

Therefore, common difference is not same so it is not an arithmetic sequence so it does not matches with OPTION C.

Now, for OPTION D, the sequence is $1, - 3,2, - 6,\ldots$ .

Here, the first term ${a_1}$ is , the second term ${a_2}$ is and third term ${a_3}$ is .

Now, check whether the common difference is same or not. If same, then the given sequence is AP else not.

$\begin{aligned}{a_2} - {a_1} = {a_3} - {a_2} \hfill\\\,\,\, - 3 - 1\mathop = \limits^? 2 + 3\hfill\\\,\,\,\,\,\,\,\,\, - 4\ne5\hfill\\\end{aligned}$

Therefore, common difference is not same so it is not an arithmetic sequence so it does not matches with OPTION D.

Thus, the arithmetic sequence is $\boxed{{\mathbf{2,4,6,8, \ldots }}}$ and it matches with $\boxed{{\mathbf{OPTION B}}}$ .

Learn more:

1. Which classification best describes the following system of equations?

2. What is the value of in the equation when ?

3. What are the values of

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Arithmetic Progression

Keywords: Common difference, linear equation, arithmetic sequence, variables, mathematics,equation of line, matches,Arithmetic Progression

Answer from: Quest

360/29

step-by-step explanation:

Answer from: Quest

(-8,5) bu tun not sure ok

Another question on Mathematics

Mathematics, 21.06.2019 19:00

Iwill give you ! what is the measure of ∠v ?

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

Mat bought a phone for $100. he has to pay $30 per mouth. if he has paid $640 in total, how many mouth has he had the phone?

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

The length of the line segment joining the midpoints of sides ab and bc of the parallelogram abcd is 10. find the length of diagnol ac

Answers: 3

Answer

Mathematics, 21.06.2019 21:10

See attachment below and find the equivalent of tan(∠qsr)

Answers: 3

Answer

You know the right answer?

Which of the following is an arithmetic sequence? a. 1, 2, 4, 8, … b. 2, 4, 6, 8, … c. 1, 2, 4, 7,...

Questions

History, 23.08.2019 23:50

(1) jack had been without a car since monday. (2) the car needed a new battery, and jack was broke. (3) although he was embarrassed, jack called his m...

Physics, 23.08.2019 23:50

Which car is accelerating? a) a car that is unmoving b) a car that rounds a curve at a constant speed c) a car that travels in st...

English, 23.08.2019 23:50

Which line in this poem indicates that the poetic speaker is hopelessly in love? love, born in greece, of late fled from his native place, forc...

Physics, 23.08.2019 23:50

What are the representative particles of elements, ionic compounds, and covalent compounds called?...

Biology, 23.08.2019 23:50

What is the control center in a cell...

History, 23.08.2019 23:50

Which of the following best describes the relationship between president wilson’s fourteen points and the treaty of versailles? a) the fourteen point...

Biology, 23.08.2019 23:50

Differentiate between response and adaption...

English, 23.08.2019 23:50

Which words in the sentence are the infinitive? when jeremy packed for camp, he was unsure how much clothing he needed to bring. a.

Mathematics, 23.08.2019 23:50

Aran moved a cone-shaped pile of sand that had a height of 4 ft and a radius of 3.2 ft. he used all of the sand to fill a cylindrical pit with a radiu...

Mathematics, 23.08.2019 23:50

What was the difference in water levels between week 2 and week 4? a. 10 m b. 1 m c. 0.10 m d. 0.01 m...

Physics, 23.08.2019 23:50

Recall that in the equilibrium position, the upward force of the spring balances the force of gravity on the weight. use this concept to estimate the...

Biology, 23.08.2019 23:50

For the body to function normally, the organs and tissues must communicate to control the development of the cells and tissues. if there is a break-do...

Mathematics, 23.08.2019 23:50

Carl has 200 songs on his mp3 player of these songs 24 are country songs what is the percent of country songs he has...

Advanced Placement (AP), 23.08.2019 23:50

Contrast the tentacles on the mole's nose when it is looking for food when it eats....

Health, 23.08.2019 23:50

When you combine alcohol with some drugs, the results can be...

Chemistry, 23.08.2019 23:50

Oxygen, nitrogen, and carbon are all metalloids nonmetals metals halogens...

English, 23.08.2019 23:50

Two poetic devices mentioned in the lecture in addition to alliteration, assonance, and onomatopoeia are rhythm and...

English, 23.08.2019 23:50

Read the sentence. i am interested in drawing, painting, and make sculpture. which is the best revision of the sentence? a. i am interested in drawin...

Mathematics, 23.08.2019 23:50

Find the quotient and remainder for 52÷8...

Biology, 23.08.2019 23:50

The basic function of a flower petal is to pollinate the ovary. a. true b. false...

More questions: Mathematics Another questions