两个不同的等差数列的第 $10$、第 $11$ 和第 $12$ 项分别为 $p+6$、$4p$ 和 $p^2$。

求这两个数列的第 $20$ 项之差。

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。

中间的第 $11$ 项等于第 $10$ 项与第 $12$ 项的平均。求出两个 $p$ 后，分别从第 $10$ 项向后数十个公差。

The condition is $2(4p)=p+6+p^2$. Thus

The common difference is $4p-(p+6)=3p-6$. The 20th term is therefore

For $p=1$ it is $-23$, and for $p=6$ it is $132$. Their difference is $132-(-23)=155$.