a_4 = \frac{4^2 + 1}{4 + 1} = \frac{16 + 1}{5} = \frac{17}{5}

February 22, 2026

$a_4 = \frac{4^2 + 1}{4 + 1} = \frac{16 + 1}{5} = \frac{17}{5}$

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a_n = \frac{n^2 + 1}{n + 1}
We attempt polynomial division or rewrite the numerator:
Note that \(n^2 + 1\) does not factor nicely over integers, so perform direct substitution for \(n = 4\):
Thus, the simplified form evaluated at \(n = 4\) is:
\boxed{\frac{17}{5}}
\]1. An electrical engineer is testing the efficiency of a new solar panel design. If a single panel produces 350 watts under ideal conditions and the system uses 24 panels, but due to shading and other losses, efficiency drops by 15%, how many usable watts does the entire system produce?

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