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

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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

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

$y\propto x$

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

Answer from: Quest

hiking down a winding trail.

step-by-step explanation:

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

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