Given that n number of arithmetic means are inserted between two pairs of numbers $a, 2 b$ and $2 a, b$; where $a, b \in R$. If the $m^{\text {th }}$ means in the two cases are the same, then the ratio $a: b$ is equal to

The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is $\mathbf{4}$, and the difference between third and fifth term is $\frac{32}{81}$, then which of the following is not true

$0.2+0.22+0.022+\ldots \ldots \ldots$. up to $n$ terms is equal to

The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in reverse order is formed. The original number is divisible by