Sure, let's solve for the given sequence step-by-step:
We start with the expression for the sequence given as:
[tex]\[
a_n = -7 + (n - 1) - 3.
\][/tex]
First, we can simplify this by combining like terms.
1. Combine [tex]\(-7\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
-7 - 3 = -10.
\][/tex]
2. Substitute this result back into the expression:
[tex]\[
a_n = -10 + (n - 1).
\][/tex]
3. Distribute and combine the terms within the parenthesis:
[tex]\[
n - 1.
\][/tex]
4. Now, combine [tex]\(-10\)[/tex] with the result from the parenthesis:
[tex]\[
a_n = n - 1 - 10.
\][/tex]
5. Simplify by combining constants:
[tex]\[
a_n = n - 11.
\][/tex]
So, the simplified form of the sequence [tex]\(a_n\)[/tex] is:
[tex]\[
a_n = n - 11.
\][/tex]
