An $A.P.$, a $G.P.$ and a $H.P.$ have the same first and last terms and the same odd number of terms. The middle terms of the three series are in
$A.P.$
$G.P.$
$H.P.$
None of these
Let $a_1, a_2, a_3, \ldots$. be a $GP$ of increasing positive numbers. If the product of fourth and sixth terms is $9$ and the sum of fifth and seventh terms is $24 ,$ then $a_1 a_9+a_2 a_4 a_9+a_5+a_7$ is equal to $.........$.
Insert three numbers between $1$ and $256$ so that the resulting sequence is a $G.P.$
If $G$ be the geometric mean of $x$ and $y$, then $\frac{1}{{{G^2} - {x^2}}} + \frac{1}{{{G^2} - {y^2}}} = $
Find a $G.P.$ for which sum of the first two terms is $-4$ and the fifth term is $4$ times the third term.
Find the sum to $n$ terms of the sequence, $8,88,888,8888 \ldots$