Amit M Agarwal Solutions for Chapter: Sequence and Series, Exercise 2: Work Book Exercise 3.2

If $a, 2b, 3c$ are in $\mathrm{AP}$ and $a, b, c$ (distinct) are in $\mathrm{GP}$, then the common ratio is

If a $\mathrm{GP}$ having an even number of terms and the sum of all terms is five times the sum of terms occupying odd places, then the common ratio will be

For $n\ge 3$, $n^{\mathrm{th}}$ roots of unity form

If $1+a+a^2+a^3+\dots +a^n=\left(1+a\right)\left(1+a^2\right)\left(1+a^4\right)$ then $n$ is equal to

The rational number $2.357357357\dots$ is

$9^{\frac{1}{3}}·9^{\frac{1}{9}}·9^{\frac{1}{27}}\dots$ is equal to

If $b_1, b_2$ and $b_3$ $\left(b_1>0\right)$ are three successive terms of a $\mathrm{GP}$ with common ratio $r$, then the possible value of $r$ for which the inequality $b_3>4b_2-3b_1$ holds, is given by

If $S$ denotes the sum to infinity and $S_n$ denotes the sum of $n$ terms of the series $1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\dots ,$ such that $S-S_n<\frac{1}{1000},$ then the least value of $n$ is