Which term of the sequence $(-8 + 18i), (-6 + 15i), (-4 + 12i), ......$ is purely imaginary (in $^{th}$)?

If $x > 1, y > 1, z > 1$ are in $G.P.$,then $\frac{1}{1 + \log x}, \frac{1}{1 + \log y}, \frac{1}{1 + \log z}$ are in

The sum of the first two terms of a $G.P.$ is $1$ and every term of this series is twice its previous term. Then,the first term will be:

Let ${T_r}$ be the ${r^{th}}$ term of an $A.P.$ for $r = 1, 2, 3, ....$. If for some positive integers $m, n$ we have ${T_m} = \frac{1}{n}$ and ${T_n} = \frac{1}{m}$,then ${T_{mn}}$ equals

Write the seventh term of the following $GP$: $6, 12, 24, 48, \ldots$

If $a_1, a_2, ..., a_n$ are positive real numbers whose product is a fixed number $c$,then the minimum value of $a_1 + a_2 + ... + a_{n-1} + 2a_n$ is