If p times the pth term of an AP is equal to q times the qth term (p ≠ q), then what is the (p + q)th term equal to? 

Let p = ln(x), q = ln(x³) and r = ln(x⁵), where x > 1. Which of the following statements is/are correct? 

I. p, q and r are in AP.

Il. p, q and r can never be in GP.

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If $\rm z=\frac{1}{3}\begin{vmatrix}i&2i&1\\\ 2i&3i&2\\\ 3&1&3\end{vmatrix}=x+iy;i=\sqrt{-1}$ then what is modulus of Z equal to?  

What is the value of the sum $\rm \sum\limits_{n=1}^{20}(i^{n-1}+i^n+i^{n+1})$ where i = √-1 ?