Question

assignment 9.1 sequences and their not
due wednesday by 11:59pm points 8 submitting an external
assignment 9.1 sequences and their notation
score: 3/8 answered: 3/8
question 4
find a formula for the general term ( a_n ) of the sequence assuming the pattern
continues.
\\( \\{ 3 , - 1 , - 5 , - 9 , - 13 , \ldots \\} \\)
assume the first term is ( a _ { 1 } )
\\( a _ { n } = \\)
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Explanation:

Step1: Identify the type of sequence

This is an arithmetic sequence. The common difference \(d\) is found by subtracting consecutive terms. For example, \(a_{2}-a_{1}=-1 - 3=-4\), \(a_{3}-a_{2}=-5-(-1)=-4\). So \(d=-4\).

Step2: Use the formula for the \(n\)th term of an arithmetic sequence

The formula for the \(n\)th term of an arithmetic sequence is \(a_{n}=a_{1}+(n - 1)d\). Here \(a_{1}=3\) and \(d=-4\).
Substitute \(a_{1}\) and \(d\) into the formula:

$$
LATEXBLOCK0
$$

Answer:

\(a_{n}=7 - 4n\)