If $(y - x),\,\,2(y - a)$ and $(y - z)$ are in $H.P.$, then $x - a,$ $y - a,$ $z - a$ are in
If $(y - x),\,\,2(y - a)$ and $(y - z)$ are in $H.P.$, then $x - a,$ $y - a,$ $z - a$ are in
- A
$A.P.$
- B
$G.P.$
- C
$H.P.$
- D
None of these
Similar Questions
The first term of an infinite geometric progression is $x$ and its sum is $5$. Then
The first term of an infinite geometric progression is $x$ and its sum is $5$. Then
- [IIT 2004]
$0.5737373...... = $
$0.5737373...... = $
Sum of infinite number of terms in $G.P.$ is $20$ and sum of their square is $100$. The common ratio of $G.P.$ is
Sum of infinite number of terms in $G.P.$ is $20$ and sum of their square is $100$. The common ratio of $G.P.$ is
- [AIEEE 2002]
Consider two G.Ps. $2,2^{2}, 2^{3}, \ldots$ and $4,4^{2}, 4^{3}, \ldots$ of $60$ and $n$ terms respectively. If the geometric mean of all the $60+n$ terms is $(2)^{\frac{225}{8}}$, then $\sum_{ k =1}^{ n } k (n- k )$ is equal to.
Consider two G.Ps. $2,2^{2}, 2^{3}, \ldots$ and $4,4^{2}, 4^{3}, \ldots$ of $60$ and $n$ terms respectively. If the geometric mean of all the $60+n$ terms is $(2)^{\frac{225}{8}}$, then $\sum_{ k =1}^{ n } k (n- k )$ is equal to.
- [JEE MAIN 2022]
Let $A _{1}, A _{2}, A _{3}, \ldots \ldots$ be an increasing geometric progression of positive real numbers. If $A _{1} A _{3} A _{5} A _{7}=\frac{1}{1296}$ and $A _{2}+ A _{4}=\frac{7}{36}$, then, the value of $A _{6}+ A _{8}+ A _{10}$ is equal to
Let $A _{1}, A _{2}, A _{3}, \ldots \ldots$ be an increasing geometric progression of positive real numbers. If $A _{1} A _{3} A _{5} A _{7}=\frac{1}{1296}$ and $A _{2}+ A _{4}=\frac{7}{36}$, then, the value of $A _{6}+ A _{8}+ A _{10}$ is equal to
- [JEE MAIN 2022]