Find the sum to the indicated number of terms in the geometric progression: $1, -a, a^{2}, -a^{3}, \ldots$ to $n$ terms (if $a \neq -1$).

If the arithmetic mean and geometric mean of the $p^{\text{th}}$ and $q^{\text{th}}$ terms of the sequence $-16, 8, -4, 2, \ldots$ satisfy the equation $4x^{2}-9x+5=0$,then $p+q$ is equal to ..... .

If $n$ geometric means between $a$ and $b$ are $G_1, G_2, ..., G_n$ and a single geometric mean is $G$,then the true relation is

If $n$ geometric means are inserted between $a$ and $b$,then the $n^{th}$ geometric mean will be:

If $a_1, a_2, a_3, \ldots, a_{10}$ is a geometric progression and $\frac{a_3}{a_1}=25$,then $\frac{a_9}{a_5}$ equals

Suppose four distinct positive numbers $a_1, a_2, a_3, a_4$ are in $G.P.$ Let $b_1=a_1, b_2=b_1+a_2, b_3=b_2+a_3$ and $b_4=b_3+a_4$.
$STATEMENT-1$ : The numbers $b_1, b_2, b_3, b_4$ are neither in $A.P.$ nor in $G.P.$
$STATEMENT-2$ : The numbers $b_1, b_2, b_3, b_4$ are in $H.P.$