138 In an arithmetic sequence with a positive first term, the sum of the first 3 terms is equal to the sum of the first 11 terms. How many terms of this sequence have the maximum sum?
A. 3
B. 4
C. 6
D. 7
138 D. Let the arithmetic sequence $\left\{a_{n}\right\}$ have the first term $a_{1}>0$, and the common difference be $d$. Then, from the condition, we get $\frac{3\left(a_{1}+a_{1}+2 \cdot d\right)}{2} = \frac{11 \cdot\left(a_{1}+a_{1}+10 \cdot d^{\prime}\right)}{2}$. Solving this, we get $d=-\frac{2}{13} \cdot a_{1}$. Given $a_{1}>0$ and $a_{n+1} \leqslant 0$, we have $1+(n-1) \cdot\left(-\frac{2}{13}\right)>0$, and $1+n \cdot\left(-\frac{2}{13}\right) \leqslant 0$. Solving these, we get $6.5 \leqslant n<7.5$, so $n=7$. Clearly, $a_{8}<0$, hence the sum of the first seven terms of the arithmetic sequence is the maximum.