To explain why 372 is not a term of the given sequence, let's follow these steps:
1. Understanding the Sequence Formula:
The formula for the nth term of the sequence is [tex]\(4n - 1\)[/tex].
2. Setting the Sequence Formula Equal to 372:
To find out if 372 is a term in the sequence, we set the formula equal to 372:
[tex]\[
4n - 1 = 372
\][/tex]
3. Solving for [tex]\(n\)[/tex]:
Rearrange the equation to solve for [tex]\(n\)[/tex]:
[tex]\[
4n = 372 + 1
\][/tex]
[tex]\[
4n = 373
\][/tex]
[tex]\[
n = \frac{373}{4}
\][/tex]
[tex]\[
n = 93.25
\][/tex]
4. Determining if [tex]\(n\)[/tex] is an Integer:
For 372 to be a term of the sequence, [tex]\(n\)[/tex] must be a positive integer because our sequence only works with integer positions. Here, [tex]\(n = 93.25\)[/tex], which is not an integer.
Since [tex]\(n\)[/tex] is not an integer, it indicates that 372 cannot be expressed in the form of [tex]\(4n - 1\)[/tex]. Therefore, 372 is not a term of this sequence.
