5.15 To plot the graph of $f(x)=a x^{2}+b x+c$, a table must be made. For values of $x$ that increase at equal intervals, the function values are successively $3844, 3969, 4096, 4227, 4356$, 4489, 4624, and 4761, one of which is incorrect:
(A) 4096.
(B) 4356.
(C) 4489.
(D) 4761.
(E) None of the above.
(3rd American High School Mathematics Examination, 1952)
[Solution] Consider the function values:
$f(x), f(x+h), f(x+2 h), \cdots, f(x+7 h), h$ are at equal intervals.

From $f(x+h)-f(x)=2 a h x+a h^{2}+b h$,
we know that the difference in function values is a linear function of $x$, i.e., it is directly proportional. In other words, the difference of the differences in function values is a constant (a second-order arithmetic sequence). Consider the differences between the following numbers:
\begin{tabular}{cccccccc}
3844 & 3969 & 4096 & 4227 & 4356 & 4489 & 4624 & 4761 \\
$\bigvee$ & $\bigvee$ & $V$ & $\bigvee$ & $\bigvee$ & $\bigvee$ & $V$ \\
125 & 127 & 131 & 129 & 133 & 135 & 137
\end{tabular}

Clearly, 4227 is the incorrect one.
Therefore, the answer is $(E)$.