Harmonic Progression

If in a $∆ABC, \sin A, \sin B, \sin C$ are in $\mathrm{A}.\mathrm{P}.,$ then –

If $\frac{\left(b+c-a\right)}{a},\frac{\left(c+a-b\right)}{b},\frac{\left(a+b-c\right)}{c}$ are in $\mathrm{AP}$, then $a,b,c$ are in

What is the relation between single harmonic mean and 'n' harmonic mean of two numbers?

If $a,b,c$ are in G.P., $a-b,c-a,b-c$ are in H.P. then $\frac{a+4b+c}{a^2+b^2}=\_\_\_\_\_$

If two harmonic means between $7$ and $8$ are $\frac{168}{23}$and $\frac{168}{22}$ then find single harmonic mean between these two numbers.

If two harmonic means between $5$ and $11$ are $\frac{55}{9}$and $\frac{55}{7}$ then the single harmonic mean between these two numbers$=$$\frac{55}{m}$, find $m$.

Three harmonic means between $1$ and $5$ are $\frac{5}{4}, \frac{5}{3}$ and _____.

Insert two harmonic means between $7 \text{and} 8$.

Find the relation among single harmonic mean and $3$ harmonic means between $\frac{1}{12} \text{and} \frac{1}{20}$.

If four harmonic means between $\frac{1}{2} \text{and} \frac{1}{22}$ are $\frac{1}{6},\frac{1}{10},\frac{1}{14},\frac{1}{18}$ then find single harmonic mean between these two numbers.

Find the sum of reciprocal of two harmonic means between $7 \text{and} 8$.

Insert three harmonic means between $2 \text{and} 3$.

Insert three harmonic means between $1 \text{and} \frac{1}{9}$.

Which term of the H.P. $1,\frac{8}{5},4,...........\text{is} \frac{-1}{8}?$

Find the ${19}^{th}$ term of the H.P. whose $5^{th}$ and ${10}^{th}$ terms are $\frac{-36}{150} \text{and} \frac{-4}{35}$ respectively.

Find the specified term of the following H.P.

${20}^{\mathrm{th}}$ term of $1,1\frac{3}{5},4,..............$

Find the specified term of the following H.P.

$6^{\mathrm{th}}$ term of $3,1\frac{1}{2},1,..............$

Find the specified term of the following H.P.

${10}^{\mathrm{th}}$ term of $1,\frac{1}{4},\frac{1}{7},\frac{1}{10},..............$

H.M. between two numbers is $4$. The A.M. $A$ and the G.M. $G$ between them satisfy the relation $2A+G^2=27$. The numbers are