Question
1. * 20 points What is the \( n \)th term of the sequence \( -1,3,7,11, \ldots \) ? A. \( a_{n}=-1-4(n-1) \) B. \( a_{n}=-1+4(n-1) \) C. \( a_{n}=4-(n-1) \) D. \( a_{n}=4+(n-1) \) Option 1 Option 2 Option 3 Option 4
Ask by Hammond Hall. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The \( n \)th term of the sequence is \( a_{n}=-1+4(n-1) \).
Solution
The first term is given by
\[
a_1 = -1.
\]
The common difference is computed by subtracting the first term from the second term:
\[
3 - (-1) = 4.
\]
For an arithmetic sequence, the \( n \)th term is given by
\[
a_n = a_1 + (n-1)d.
\]
Substituting \( a_1 = -1 \) and \( d = 4 \):
\[
a_n = -1 + 4(n-1).
\]
Thus, the correct answer is Option 2:
\[
a_{n}=-1+4(n-1).
\]
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Simplify this solution Mind Expander
The sequence given is \( -1, 3, 7, 11, \ldots \). If we look closely, we can see that it is increasing by 4 for each subsequent term. To find the \( n \)th term, we start from -1 and add \( 4(n-1) \) because \( n-1 \) gives us the number of jumps of 4 we need to make after the first term. Thus, the correct formula is \( a_n = -1 + 4(n-1) \). The correct answer is: **B. \( a_{n}=-1+4(n-1) \)** With clear patterns in sequences like this, it's like solving a puzzle! Just remember to identify the common difference, and you’ll get the hang of it quickly! And if you ever feel unsure, don’t hesitate to graph the terms—visuals can make it all click!
