alexwing285
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Which of the following is true regarding the sequence below?
7/12, 1/6, -1/4, 2/3
A. The sequence is arithmetic because there is a common difference of -5/12
B. The sequence is arithmetic because there is a common difference of 1.
C. The sequence is not arithmetic because there is no common difference between the values of n.
D. The sequence is not arithmetic because there is no common difference between the values of a_n.

Respuesta :

Answer: Option D

Explanation:

Arithmetic Progression is the sequence of numbers in which consecutive terms have same or common difference.

common difference d= a2-a1

Option A is incorrect because in last two terms there is not a common difference of [tex]\frac{-5}{12}[/tex]

[tex]\frac{1}{6} -\frac{7}{12} =\frac{-5}{12}[/tex] , [tex]\frac{-1}{4} -\frac{1}{6} =\frac{-5}{12}[/tex] , [tex]\frac{2}{3} -\frac{-1}{4} =\frac{11}{12}[/tex].

Option B is incorrect because there is not a common difference of 1 in any of the given terms

Option C is incorrect because we do not check common difference in the number of terms that is n we check it for [tex]a_{n}[/tex].



facundo3141592

We will see that the correct statement is D:

"The sequence is not arithmetic because there is no common difference between the values of a_n."

What type of sequence do we have?

Here we have the sequence:

7/12, 1/6, -1/4, 2/3

First, remember that for an arithmetic sequence we have the relation:

[tex]a_n = a_{n-1} + d[/tex]

Where d is the common difference.

Here you can see that the second term is positive and the third is negative, so you would expect to have a negative common difference.

But then the fourth term is positive, so this time we go from a negative term to a positive one, so this would imply that the common difference is positive.

Thus, this can't be an arithmetic sequence, because the common difference (that should be the same for the whole sequence) can't take two signs.

So we can conclude that the correct option is D:

"The sequence is not arithmetic because there is no common difference between the values of a_n."

If you want to learn more about sequences, you can read:

https://brainly.com/question/6561461

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