Answered

Expand your horizons with the diverse and informative answers found on IDNLearn.com. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.

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]."
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.