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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]



Answer :

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.

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