G Tewani Solutions for Chapter: Progression and Series, Exercise 1: Exercises

If $p,q,$ and $r$ are in A.P. then which of the following is/are true?

If $x^2+9y^2+25z^2=xyz \left(\frac{15}{x}+\frac{5}{y}+\frac{3}{z}\right)$, then

If $A_1,A_2,G_1,G_2$ and $H_1 , H_2$ are two arithemetic, geometric and harmonic means, respectively, between two qualities $a$ and $b$, then $ab$ is equal to

If $\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c}$, then which of the following is/are possible?

If $a,b,c$ are three distinct numbers in G.P., $b,c,a$ are in A.P., and $a,bc,abc$ are in H.P., then the possible value of $b$ is

If $a,b,c$ are in A.P. and $a^2,b^2,c^2$ are in H.P. Then, which is of the following is/are possible?

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

Let $E=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+....,$ Then,