Amit M Agarwal Solutions for Chapter: Sequence and Series, Exercise 5: Target Exercises

If $\cos \left(x-y\right),\cos x$ and $\cos \left(x+y\right)$ are in $\mathrm{HP}$, then $\cos x\sec \left(\frac{y}{2}\right)$ is equal to

${\log }_{3}2,{\log }_{6}2$ and ${\log }_{12}2$ are in

If $a,b$ and $c$ are in $\mathrm{HP}$, then correct statement is

The $\mathrm{AM}, \mathrm{GM}$ and $\mathrm{HM}$ of two numbers are $x, y$ and $z$, respectively. Then, which of the following is true?

If $a,b$ and $c$ are in $\mathrm{HP}$, then the straight line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ always passes through a fixed point and that point is

Let $a_1,a_2,\dots ,a_{10}$ be in $\mathrm{AP}$ and $h_1,h_2,\dots ,h_{10}$ be in $\mathrm{HP}$. If $a_1=h_1=2$ and $a_{10}=h_{10}=3$, then $a_4{h}_7$ is

If $x,y$ and $z$ are in $\mathrm{HP}$, where $z>y>x$. Then, value of $\log \left(x+z\right)+\log \left(x-2y+z\right)$ is

If $H_1,H_2,H_3,\dots ,H_{2n+1}$ are in $\mathrm{HP}$, then $\sum _{i=1}^{2n}{\left(-1\right)}^i\left(\frac{H_i+H_{i+1}}{H_i-H_{i+1}}\right)$ is equal to