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Which is true regarding the sequence below?
[tex]\[ 5, 2, -3, -10, -19 \][/tex]

A. The sequence is arithmetic because the common difference is -1.
B. The sequence is arithmetic because the common difference is 1.
C. The sequence is not arithmetic because there is no common difference. The differences are [tex]\(-3, -5, -7\)[/tex].
D. The sequence is not arithmetic because there is no common difference. The differences are [tex]\(-\frac{1}{3}, -\frac{1}{5}, -\frac{1}{7}\)[/tex], and [tex]\(-\frac{1}{9}\)[/tex].

Sagot :

GinnyAnsweridn
Let's analyze the given sequence step by step to determine which statement is correct:

The given sequence is:
[tex]\[ 5, 2, -3, -10, -19 \][/tex]

To determine whether the sequence is arithmetic, we need to calculate the differences between each pair of consecutive terms. An arithmetic sequence has a constant common difference between each consecutive term.

1. Calculate the difference between the first and second terms:
[tex]\[ 2 - 5 = -3 \][/tex]
So, the difference between the first and second terms is [tex]\(-3\)[/tex].

2. Calculate the difference between the second and third terms:
[tex]\[ -3 - 2 = -5 \][/tex]
So, the difference between the second and third terms is [tex]\(-5\)[/tex].

3. Calculate the difference between the third and fourth terms:
[tex]\[ -10 - (-3) = -10 + 3 = -7 \][/tex]
So, the difference between the third and fourth terms is [tex]\(-7\)[/tex].

4. Calculate the difference between the fourth and fifth terms:
[tex]\[ -19 - (-10) = -19 + 10 = -9 \][/tex]
So, the difference between the fourth and fifth terms is [tex]\(-9\)[/tex].

The differences between the consecutive terms are:
[tex]\[ -3, -5, -7, -9 \][/tex]

Since the differences are not consistent, there is no common difference. Therefore, the sequence is not arithmetic.

So, the correct statement is:
"The sequence is not arithmetic because there is no common difference. The differences are [tex]\(-3, -5, -7\)[/tex] and [tex]\(-9\)[/tex]."
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