Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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.
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.