To determine if -58 is a term in the sequence whose [tex]$n$[/tex]th term is given by [tex]\( 8 - 6n \)[/tex], we need to find an integer value of [tex]\( n \)[/tex] such that the term in the sequence equals -58. Let's follow these steps:
1. Set the [tex]$n$[/tex]th term equal to -58:
[tex]\[
8 - 6n = -58
\][/tex]
2. Solve for [tex]\( n \)[/tex].
First, isolate the term [tex]\(-6n\)[/tex] by subtracting 8 from both sides of the equation:
[tex]\[
-6n = -58 - 8
\][/tex]
Simplify the right-hand side:
[tex]\[
-6n = -66
\][/tex]
3. Next, solve for [tex]\( n \)[/tex] by dividing both sides by -6:
[tex]\[
n = \frac{-66}{-6}
\][/tex]
Simplify the division:
[tex]\[
n = 11
\][/tex]
4. Verify if [tex]\( n = 11 \)[/tex] is an integer. Indeed, [tex]\( n = 11 \)[/tex] is a positive integer.
Therefore, since [tex]\( n = 11 \)[/tex] is an integer, -58 is a term of the sequence [tex]\( 8 - 6n \)[/tex].
