If $a,\;b,\;c$ are in $G.P.$, $a - b,\;c - a,\;b - c$ are in $H.P.$, then $a + 4b + c$ is equal to

For the two positive numbers $a , b$, if $a , b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{ a }, 10$ and $\frac{1}{ b }$ are in an arithmetic progression, then, $16 a+12 b$ is equal to $.........$.

The sum of three consecutive terms in a geometric progression is $14$. If $1$ is added to the first and the second terms and $1$ is subtracted from the third, the resulting new terms are in arithmetic progression. Then the lowest of the original term is

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 $4 x^{2}-9 x+5=0,$ then $p+q$ is equal to ..... .

If the ${(m + 1)^{th}},\;{(n + 1)^{th}}$ and ${(r + 1)^{th}}$ terms of an $A.P.$ are in $G.P.$ and $m,\;n,\;r$ are in $H.P.$, then the value of the ratio of the common difference to the first term of the $A.P.$ is

If $a,\;b,\;c$ are in $G.P.$ and $x,\,y$ are the arithmetic means between $a,\;b$ and $b,\;c$ respectively, then $\frac{a}{x} + \frac{c}{y}$ is equal to