Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Question 3 (Multiple Choice Worth 2 points)

What is the equation for the [tex]$n$[/tex]th term of the arithmetic sequence where [tex]$a_1 = 28$[/tex] and [tex]$d = -6$[/tex]?

A. [tex]$a_n = 28 - 6n$[/tex]
B. [tex]$a_n = 28 + 6n$[/tex]
C. [tex]$a_n = 28 + 6(n-1)$[/tex]
D. [tex]$a_n = 28 - 6(n-1)$[/tex]

Sagot :

GinnyAnswer
To find the equation for the \( n \)th term of an arithmetic sequence, we need to use the following formula for the \( n \)th term \( a_n \):

[tex]\[ a_n = a_1 + (n-1)d \][/tex]

Where:
- \( a_1 \) is the first term of the sequence.
- \( d \) is the common difference between the terms.
- \( n \) is the term number.

Given:
- The first term \( a_1 = 28 \)
- The common difference \( d = -6 \)

Let's substitute these values into the formula:

[tex]\[ a_n = 28 + (n-1)(-6) \][/tex]

Next, simplify the expression inside the parentheses:

[tex]\[ a_n = 28 + (-6)(n-1) \][/tex]

Now distribute the \(-6\):

[tex]\[ a_n = 28 - 6(n-1) \][/tex]

Thus, the equation for the \( n \)th term of the arithmetic sequence is:

[tex]\[ a_n = 28 - 6(n-1) \][/tex]

This matches the fourth option provided in the multiple-choice question. Therefore, the answer is:

[tex]\[ \boxed{a_n = 28 - 6(n-1)} \][/tex]

And hence, the correct option is the fourth one.
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.