R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 7: VERY SHORT ANSWER QUESTIONS (VSAQs)

If $(p+q{)}^{th}$ and $(p-q{)}^{th}$ terms of a G.P. are $m$ and $n$ respectively, then write its $p^{th}$ term.

If ${\log }_{x}a, a^{x/2}$ and ${\log }_{b}x$ are in G.P., then write the value of $x$.

If $p^{\text{th }}, q^{\text{th }}$ and $r^{\text{th }}$ terms of a G.P. are $x, y, z$ respectively, then write the value of $x^{q-r}{y}^{r-p}{z}^{p-q}$.

If $A_1, A_2$ be two AM's and $G_1, G_2$ be two GM's between $a$ and $b$, then find the value of $\frac{A_1+A_2}{G_1{G}_2}$

If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.

Write the quadratic equation the arithmetic and geometric means of whose roots are $A$and $G$ respectively.

Write the product of $n$ geometric means between two numbers $a$ and $b$.

If $a=1+b+b^2+b^3+\dots$ to $\infty ,$ then write $b$ in terms of $a$ given that $\left|b\right|<1$