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