To find the algebraic expression that represents the nth number in the sequence \(26, 22, 18, 14, 10, 6\), we first observe the pattern in the sequence:
- The sequence starts at 26.
- Each subsequent term decreases by 4.
This indicates that the sequence is linear and can be expressed in the form of \(a_n = an + b\), where \(a\) is the common difference and \(b\) is the first term.
- Identify the common difference: The difference between consecutive terms is \(22 - 26 = -4\), \(18 - 22 = -4\), etc. So, the common difference \(a = -4\).
- Initial term: The first term of the sequence (\(n=1\)) is \(26\).
Thus, we can write the expression for the nth term like so:
\[ a_n = -4n + b \]
To find \(b\), we set \(n=1\): \[ a_1 = -4(1) + b = 26 \] \[ -4 + b = 26 \implies b = 30 \]
So the algebraic expression for the nth term is:
\[ a_n = -4n + 30 \]
Now, we can match this expression to the options given:
A. \(-4n + 26\)
B. \(4n + 22\)
C. \(26n - 4\)
D. \(-4n + 30\)
The correct answer is:
D. \(-4n + 30\).