一个等差数列的第十三项为 $12$，前 $30$ 项的和为 $-15$。

求这个数列的前 $50$ 项的和。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

把第 $13$ 项和前 $30$ 项和分别写成首项、公差的方程。解出两者后再求前 $50$ 项和。

Let the first term be $a$ and the common difference be $d$. The conditions give

Thus $2a+29d=-1$. Subtracting twice the first equation gives $5d=-25$, so $d=-5$ and $a=72$. Therefore