Interval in which q lies.Let $a_{i}=i+\frac{1}{i}$.Put $p=\frac{1}{20}\sum_{k=1}^{20}a_{k}$and$q=\frac{1}{20}\sum_{k=1}^{20}\frac{1}{a_{k}}$

Let $ $ a_{i}=i+\frac{1}{i}$ $ for $ i=1,2,3…,20$ .

Put $ $ p=\frac{1}{20}\left(a_{1}+a_{2}+…+a_{20}\right)$ $ and$ $ q=\frac{1}{20}\left(\frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}+…+\frac{1}{a_{20}}\right)$ $ Then which of the following is correct

$ (A)q\in\left(0,\frac{22-p}{21}\right)$

$ (B)q\in\left(\frac{22-p}{21},\frac{2(22-p)}{21}\right)$

$ (C)q\in\left(\frac{2(22-p)}{21},\frac{2(22-p)}{7}\right)$

$ (D)q\in\left(\frac{22-p}{7},\frac{4(22-p)}{21}\right)$

It appears to be question involving A.M>H.M