Ans: A
Let $a$ and $d$ be the first term and the common difference of the sequence respectively.
Let $a$ and $d$ be the first term and the common difference of the sequence respectively.
It is given that $a_{18}=26$ and $a_{23}=61$, then we have
$\left\{ \begin{array}{ll}
a+17d = 26 & \ldots \unicode{x2460} \\
a+22d = 61 & \ldots \unicode{x2461}
\end{array}\right.$
$\unicode{x2461} – \unicode{x2460}$, we have
$\begin{array}{rcl}
5d & = & 35 \\
d & = & 7
\end{array}$
Sub. $d=7$ into $\unicode{x2460}$, we have
$\begin{array}{rcl}
a+17(7) & = & 26 \\
a & = & -93
\end{array}$
Hence, $a_n=-93+(n-1)7=7n-100$.
I is true. $a_{14}=7(14)-100=-2$.
II is true. Since $a_2-a_1=7$, then $a_1-a_2=-7<0$.
III is false. Consider the sum of the first 27 terms, we have
$\begin{array}{cl}
& S(27) \\
= & \dfrac{27}{2}[2(-93)+(27-1)7] \\
= & -54 \\
< & 0
\end{array}$
