Let $a, b, c$ be positive integers such that $\frac{b}{a}$ is an integer. If $a, b, c$ are in geometric progression and the arithmetic mean of $a, b, c$ is $b+2$, then the value of $\frac{a^2+a-14}{a+1}$ is

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

Let three real numbers $a, b, c$ be in arithmetic progression and $\mathrm{a}+1, \mathrm{~b}, \mathrm{c}+3$ be in geometric progression. If $\mathrm{a}>10$ and the arithmetic mean of $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ is $8$ , then the cube of the geometric mean of $a, b$ and $c$ is

If the first and ${(2n - 1)^{th}}$ terms of an $A.P., G.P.$ and $H.P.$ are equal and their ${n^{th}}$ terms are respectively $a,\;b$ and $c$, then

In a $G.P.$ the sum of three numbers is $14$, if $1 $ is added to first two numbers and subtracted from third number, the series becomes $A.P.$, then the greatest number is

If the product of three terms of $G.P.$ is $512$. If $8$ added to first and $6$ added to second term, so that number may be in $A.P.$, then the numbers are