Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine the common difference in an arithmetic sequence, we need to subtract each term from the following term and check if the difference remains constant throughout the sequence.
Consider the sequence: [tex]\(9, 2.5, -4, -10.5, -17, \ldots\)[/tex]
1. Calculate the difference between the first and second terms:
[tex]\[ 2.5 - 9 = -6.5 \][/tex]
2. Calculate the difference between the second and third terms:
[tex]\[ -4 - 2.5 = -6.5 \][/tex]
3. Calculate the difference between the third and fourth terms:
[tex]\[ -10.5 - (-4) = -10.5 + 4 = -6.5 \][/tex]
4. Calculate the difference between the fourth and fifth terms:
[tex]\[ -17 - (-10.5) = -17 + 10.5 = -6.5 \][/tex]
We observe that the difference between each pair of successive terms is consistently [tex]\(-6.5\)[/tex]. Therefore, the common difference in the sequence is [tex]\(-6.5\)[/tex].
So, among the given choices, the common difference is:
[tex]\(\boxed{-6.5}\)[/tex]
Consider the sequence: [tex]\(9, 2.5, -4, -10.5, -17, \ldots\)[/tex]
1. Calculate the difference between the first and second terms:
[tex]\[ 2.5 - 9 = -6.5 \][/tex]
2. Calculate the difference between the second and third terms:
[tex]\[ -4 - 2.5 = -6.5 \][/tex]
3. Calculate the difference between the third and fourth terms:
[tex]\[ -10.5 - (-4) = -10.5 + 4 = -6.5 \][/tex]
4. Calculate the difference between the fourth and fifth terms:
[tex]\[ -17 - (-10.5) = -17 + 10.5 = -6.5 \][/tex]
We observe that the difference between each pair of successive terms is consistently [tex]\(-6.5\)[/tex]. Therefore, the common difference in the sequence is [tex]\(-6.5\)[/tex].
So, among the given choices, the common difference is:
[tex]\(\boxed{-6.5}\)[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.